Codebase list eclib / ee9aaa7
New upstream version 20161230 Julien Puydt 7 years ago
6 changed file(s) with 607 addition(s) and 19 deletion(s). Raw diff Collapse all Expand all
+2
-2
configure.ac less more
22 # Process this file with autoconf to produce a configure script.
33
44 AC_PREREQ([2.65])
5 AC_INIT([eclib], [20161223], [john.cremona@gmail.com])
5 AC_INIT([eclib], [20161230], [john.cremona@gmail.com])
66 AM_INIT_AUTOMAKE([-Wall])
77 AC_MSG_NOTICE([Configuring eclib...])
88 AC_CONFIG_SRCDIR([libsrc])
3535 # NB The suffix of the library name (libec.so here) is (c-a).a.r
3636
3737 LT_CURRENT=3
38 LT_REVISION=1
38 LT_REVISION=2
3939 LT_AGE=0
4040 AC_SUBST(LT_CURRENT)
4141 AC_SUBST(LT_REVISION)
+4
-2
libsrc/newforms.cc less more
18491849 {
18501850 rational a(h1->nfproj_coords(num(r),den(r),nflist[i].coordsplus),
18511851 nflist[i].cuspidalfactorplus);
1852 if (base_at_infinity) a-=nflist[i].loverp;
1852 // {oo,r} = {0,r}+{oo,0} and loverp={oo,0} (not {0,oo}!)
1853 if (base_at_infinity) a+=nflist[i].loverp;
18531854 a *= nflist[i].optimalityfactorplus;
18541855 return a;
18551856 }
18701871 m.setcol(2,nflist[i].coordsminus);
18711872 vec a = h1->proj_coords(num(r),den(r),m);
18721873 rational a1(a[1],nflist[i].cuspidalfactorplus);
1873 if (base_at_infinity) a1 -= nflist[i].loverp;
1874 // {oo,r} = {0,r}+{oo,0} and loverp={oo,0} (not {0,oo}!)
1875 if (base_at_infinity) a1 += nflist[i].loverp;
18741876 a1 *= nflist[i].optimalityfactorplus;
18751877 rational a2(a[2],nflist[i].cuspidalfactorminus);
18761878 a2 *= nflist[i].optimalityfactorminus;
+19
-11
progs/ecnf.cc less more
3030 #include <eclib/cperiods.h>
3131 #include <eclib/newforms.h>
3232 #include <eclib/curve.h>
33 #include <eclib/getcurve.h>
3334
3435 int main(void)
3536 {
3637 int verbose=0;
38 vector<bigrational> ai(5);
39 bigint v;
3740
38 // Read in the curve, minimise and construct CurveRed (needed for
41 // Read in curves, minimise and construct CurveRed (needed for
3942 // conductor and Traces of Frobenius etc.)
40 Curve C;
41 cout << "Enter curve: "; cin >> C;
42 Curvedata CD(C,1); // minimise
43 CurveRed CR(CD);
44 bigint N = getconductor(CR);
45 int n = I2int(N);
46 cout << ">>> Level = conductor = " << n << " <<<" << endl;
47 cout << "Minimal curve = " << (Curve)(CR) << endl;
48 cout<<endl;
43 while (getcurve(ai,verbose))
44 {
45 Curvedata CD(ai,v);
46 CurveRed CR(CD);
47 bigint N = getconductor(CR);
48 int n = I2int(N);
49 cout << ">>> Level = conductor = " << n << " <<<" << endl;
50 cout << "Minimal curve = " << (Curve)(CR) << endl;
51 cout<<endl;
4952
5053 // Construct newforms class (this does little work)
5154 int sign=1;
6467 cout<<endl;
6568
6669 // Display modular symbol info
67 cout << "Modular symbol map:"<<endl;
70 cout << "Modular symbol map (";
71 if (sign!=-1) cout << "+";
72 if (sign==0) cout << ",";
73 if (sign!=1) cout << "-";
74 cout << ")" << endl;
6875 nf.display_modular_symbol_map();
6976
7077 // Compute more modular symbols as prompted:
114121 }
115122 }
116123 }
124 } // end of curve input loop
117125 } // end of main()
+30
-0
progs/in/ecnf.in less more
0 [0,-1,1,-10,-20]
1 0
2 0
3 0 0
4 5
5 [0,-1,1,-10,-20]
6 1
7 0
8 0 0
9 5
10 [0,-1,1,-10,-20]
11 0
12 1
13 0 0
14 5
15 [0,-1,1,-10,-20]
16 1
17 1
18 0 0
19 5
20 [0,-1,1,0,0]
21 0
22 0
23 0 0
24 5
25 [0, -1, 1, -7820, -263580]
26 0
27 0
28 0 0
29 5
030 [0,1,1,-2,0]
131 0
232 1
+276
-2
progs/out_no_ntl/ecnf.out less more
0 Enter curve: >>> Level = conductor = 389 <<<
0 >>> Level = conductor = 11 <<<
1 Minimal curve = [0,-1,1,-10,-20]
2
3 Enter sign (1,-1,0 for both):Newform information:
4
5 1 newform(s) at level 11:
6 p0=2
7 #ap= 100
8 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
9 aq = [ -1 ]
10 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
11 SFE = 1, L/P = 2/5
12 lplus = 1, mplus = 1
13 lminus = 3, mminus = -2
14 [(4,1;1,3),1,1;1]
15
16 Modular symbol map (+,-)
17 (0:1) = {0,oo} -> (-2/5,0)
18 (1:1) = {0,1} -> (0,0)
19 (2:1) = {0,1/2} -> (-2,0)
20 (3:1) = {0,1/3} -> (-1,-1)
21 (4:1) = {0,1/4} -> (1,-1)
22 (5:1) = {0,1/5} -> (2,0)
23 (6:1) = {0,1/6} -> (2,0)
24 (7:1) = {0,1/7} -> (1,1)
25 (8:1) = {0,1/8} -> (-1,1)
26 (9:1) = {0,1/9} -> (-2,0)
27 (10:1) = {0,1/10} -> (0,0)
28 (1:0) = {oo,0} -> (2/5,0)
29
30 Computation of further modular symbols
31
32 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
33 Enter numerator and denominator of r:
34 All modular symbols with bounded denominator
35
36 Enter maximum denominator (0 for none): {0,0} -> (0,0)
37 {0,1/2} -> (-2,0)
38 {0,1/3} -> (-1,-1)
39 {0,2/3} -> (-1,1)
40 {0,1/4} -> (1,-1)
41 {0,3/4} -> (1,1)
42 {0,1/5} -> (2,0)
43 {0,2/5} -> (-3,-1)
44 {0,3/5} -> (-3,1)
45 {0,4/5} -> (2,0)
46 >>> Level = conductor = 11 <<<
47 Minimal curve = [0,-1,1,-10,-20]
48
49 Enter sign (1,-1,0 for both):Newform information:
50
51 1 newform(s) at level 11:
52 p0=2
53 #ap= 100
54 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
55 aq = [ -1 ]
56 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
57 SFE = 1, L/P = 2/5
58 lplus = 1, mplus = 1
59 [(-5,1;-1,2),2,0;?]
60
61 Modular symbol map (+)
62 (0:1) = {0,oo} -> -2/5
63 (1:1) = {0,1} -> 0
64 (2:1) = {0,1/2} -> -2
65 (3:1) = {0,1/3} -> -1
66 (4:1) = {0,1/4} -> 1
67 (5:1) = {0,1/5} -> 2
68 (6:1) = {0,1/6} -> 2
69 (7:1) = {0,1/7} -> 1
70 (8:1) = {0,1/8} -> -1
71 (9:1) = {0,1/9} -> -2
72 (10:1) = {0,1/10} -> 0
73 (1:0) = {oo,0} -> 2/5
74
75 Computation of further modular symbols
76
77 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
78 Enter numerator and denominator of r:
79 All modular symbols with bounded denominator
80
81 Enter maximum denominator (0 for none): {0,0} -> 0
82 {0,1/2} -> -2
83 {0,1/3} -> -1
84 {0,2/3} -> -1
85 {0,1/4} -> 1
86 {0,3/4} -> 1
87 {0,1/5} -> 2
88 {0,2/5} -> -3
89 {0,3/5} -> -3
90 {0,4/5} -> 2
91 >>> Level = conductor = 11 <<<
92 Minimal curve = [0,-1,1,-10,-20]
93
94 Enter sign (1,-1,0 for both):Newform information:
95
96 1 newform(s) at level 11:
97 p0=2
98 #ap= 100
99 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
100 aq = [ -1 ]
101 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
102 SFE = 1, L/P = 2/5
103 lplus = 1, mplus = 1
104 lminus = 3, mminus = -2
105 [(4,1;1,3),1,1;1]
106
107 Modular symbol map (+,-)
108 (0:1) = {0,oo} -> (-2/5,0)
109 (1:1) = {0,1} -> (0,0)
110 (2:1) = {0,1/2} -> (-2,0)
111 (3:1) = {0,1/3} -> (-1,-1)
112 (4:1) = {0,1/4} -> (1,-1)
113 (5:1) = {0,1/5} -> (2,0)
114 (6:1) = {0,1/6} -> (2,0)
115 (7:1) = {0,1/7} -> (1,1)
116 (8:1) = {0,1/8} -> (-1,1)
117 (9:1) = {0,1/9} -> (-2,0)
118 (10:1) = {0,1/10} -> (0,0)
119 (1:0) = {oo,0} -> (2/5,0)
120
121 Computation of further modular symbols
122
123 Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
124 Enter numerator and denominator of r:
125 All modular symbols with bounded denominator
126
127 Enter maximum denominator (0 for none): {oo,0} -> (2/5,0)
128 {oo,1/2} -> (-8/5,0)
129 {oo,1/3} -> (-3/5,-1)
130 {oo,2/3} -> (-3/5,1)
131 {oo,1/4} -> (7/5,-1)
132 {oo,3/4} -> (7/5,1)
133 {oo,1/5} -> (12/5,0)
134 {oo,2/5} -> (-13/5,-1)
135 {oo,3/5} -> (-13/5,1)
136 {oo,4/5} -> (12/5,0)
137 >>> Level = conductor = 11 <<<
138 Minimal curve = [0,-1,1,-10,-20]
139
140 Enter sign (1,-1,0 for both):Newform information:
141
142 1 newform(s) at level 11:
143 p0=2
144 #ap= 100
145 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
146 aq = [ -1 ]
147 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
148 SFE = 1, L/P = 2/5
149 lplus = 1, mplus = 1
150 [(-5,1;-1,2),2,0;?]
151
152 Modular symbol map (+)
153 (0:1) = {0,oo} -> -2/5
154 (1:1) = {0,1} -> 0
155 (2:1) = {0,1/2} -> -2
156 (3:1) = {0,1/3} -> -1
157 (4:1) = {0,1/4} -> 1
158 (5:1) = {0,1/5} -> 2
159 (6:1) = {0,1/6} -> 2
160 (7:1) = {0,1/7} -> 1
161 (8:1) = {0,1/8} -> -1
162 (9:1) = {0,1/9} -> -2
163 (10:1) = {0,1/10} -> 0
164 (1:0) = {oo,0} -> 2/5
165
166 Computation of further modular symbols
167
168 Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
169 Enter numerator and denominator of r:
170 All modular symbols with bounded denominator
171
172 Enter maximum denominator (0 for none): {oo,0} -> 2/5
173 {oo,1/2} -> -8/5
174 {oo,1/3} -> -3/5
175 {oo,2/3} -> -3/5
176 {oo,1/4} -> 7/5
177 {oo,3/4} -> 7/5
178 {oo,1/5} -> 12/5
179 {oo,2/5} -> -13/5
180 {oo,3/5} -> -13/5
181 {oo,4/5} -> 12/5
182 >>> Level = conductor = 11 <<<
183 Minimal curve = [0,-1,1,0,0]
184
185 Enter sign (1,-1,0 for both):Newform information:
186
187 1 newform(s) at level 11:
188 p0=2
189 #ap= 100
190 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
191 aq = [ -1 ]
192 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
193 SFE = 1, L/P = 2/5
194 lplus = 1, mplus = 1
195 lminus = 3, mminus = -2
196 [(4,1;1,3),1,1;1]
197
198 Modular symbol map (+,-)
199 (0:1) = {0,oo} -> (-2/25,0)
200 (1:1) = {0,1} -> (0,0)
201 (2:1) = {0,1/2} -> (-2/5,0)
202 (3:1) = {0,1/3} -> (-1/5,-1)
203 (4:1) = {0,1/4} -> (1/5,-1)
204 (5:1) = {0,1/5} -> (2/5,0)
205 (6:1) = {0,1/6} -> (2/5,0)
206 (7:1) = {0,1/7} -> (1/5,1)
207 (8:1) = {0,1/8} -> (-1/5,1)
208 (9:1) = {0,1/9} -> (-2/5,0)
209 (10:1) = {0,1/10} -> (0,0)
210 (1:0) = {oo,0} -> (2/25,0)
211
212 Computation of further modular symbols
213
214 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
215 Enter numerator and denominator of r:
216 All modular symbols with bounded denominator
217
218 Enter maximum denominator (0 for none): {0,0} -> (0,0)
219 {0,1/2} -> (-2/5,0)
220 {0,1/3} -> (-1/5,-1)
221 {0,2/3} -> (-1/5,1)
222 {0,1/4} -> (1/5,-1)
223 {0,3/4} -> (1/5,1)
224 {0,1/5} -> (2/5,0)
225 {0,2/5} -> (-3/5,-1)
226 {0,3/5} -> (-3/5,1)
227 {0,4/5} -> (2/5,0)
228 >>> Level = conductor = 11 <<<
229 Minimal curve = [0,-1,1,-7820,-263580]
230
231 Enter sign (1,-1,0 for both):Newform information:
232
233 1 newform(s) at level 11:
234 p0=2
235 #ap= 100
236 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
237 aq = [ -1 ]
238 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
239 SFE = 1, L/P = 2/5
240 lplus = 1, mplus = 1
241 lminus = 3, mminus = -2
242 [(4,1;1,3),1,1;1]
243
244 Modular symbol map (+,-)
245 (0:1) = {0,oo} -> (-2,0)
246 (1:1) = {0,1} -> (0,0)
247 (2:1) = {0,1/2} -> (-10,0)
248 (3:1) = {0,1/3} -> (-5,-1)
249 (4:1) = {0,1/4} -> (5,-1)
250 (5:1) = {0,1/5} -> (10,0)
251 (6:1) = {0,1/6} -> (10,0)
252 (7:1) = {0,1/7} -> (5,1)
253 (8:1) = {0,1/8} -> (-5,1)
254 (9:1) = {0,1/9} -> (-10,0)
255 (10:1) = {0,1/10} -> (0,0)
256 (1:0) = {oo,0} -> (2,0)
257
258 Computation of further modular symbols
259
260 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
261 Enter numerator and denominator of r:
262 All modular symbols with bounded denominator
263
264 Enter maximum denominator (0 for none): {0,0} -> (0,0)
265 {0,1/2} -> (-10,0)
266 {0,1/3} -> (-5,-1)
267 {0,2/3} -> (-5,1)
268 {0,1/4} -> (5,-1)
269 {0,3/4} -> (5,1)
270 {0,1/5} -> (10,0)
271 {0,2/5} -> (-15,-1)
272 {0,3/5} -> (-15,1)
273 {0,4/5} -> (10,0)
274 >>> Level = conductor = 389 <<<
1275 Minimal curve = [0,1,1,-2,0]
2276
3277 Enter sign (1,-1,0 for both):Newform information:
13287 lminus = 3, mminus = -4
14288 [(-111,1;-2,7),1,1;2]
15289
16 Modular symbol map:
290 Modular symbol map (+,-)
17291 (0:1) = {0,oo} -> (0,0)
18292 (1:1) = {0,1} -> (0,0)
19293 (2:1) = {0,1/2} -> (0,0)
+276
-2
progs/out_ntl/ecnf.out less more
0 Enter curve: >>> Level = conductor = 389 <<<
0 >>> Level = conductor = 11 <<<
1 Minimal curve = [0,-1,1,-10,-20]
2
3 Enter sign (1,-1,0 for both):Newform information:
4
5 1 newform(s) at level 11:
6 p0=2
7 #ap= 100
8 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
9 aq = [ -1 ]
10 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
11 SFE = 1, L/P = 2/5
12 lplus = 1, mplus = 1
13 lminus = 3, mminus = -2
14 [(4,1;1,3),1,1;1]
15
16 Modular symbol map (+,-)
17 (0:1) = {0,oo} -> (-2/5,0)
18 (1:1) = {0,1} -> (0,0)
19 (2:1) = {0,1/2} -> (-2,0)
20 (3:1) = {0,1/3} -> (-1,-1)
21 (4:1) = {0,1/4} -> (1,-1)
22 (5:1) = {0,1/5} -> (2,0)
23 (6:1) = {0,1/6} -> (2,0)
24 (7:1) = {0,1/7} -> (1,1)
25 (8:1) = {0,1/8} -> (-1,1)
26 (9:1) = {0,1/9} -> (-2,0)
27 (10:1) = {0,1/10} -> (0,0)
28 (1:0) = {oo,0} -> (2/5,0)
29
30 Computation of further modular symbols
31
32 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
33 Enter numerator and denominator of r:
34 All modular symbols with bounded denominator
35
36 Enter maximum denominator (0 for none): {0,0} -> (0,0)
37 {0,1/2} -> (-2,0)
38 {0,1/3} -> (-1,-1)
39 {0,2/3} -> (-1,1)
40 {0,1/4} -> (1,-1)
41 {0,3/4} -> (1,1)
42 {0,1/5} -> (2,0)
43 {0,2/5} -> (-3,-1)
44 {0,3/5} -> (-3,1)
45 {0,4/5} -> (2,0)
46 >>> Level = conductor = 11 <<<
47 Minimal curve = [0,-1,1,-10,-20]
48
49 Enter sign (1,-1,0 for both):Newform information:
50
51 1 newform(s) at level 11:
52 p0=2
53 #ap= 100
54 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
55 aq = [ -1 ]
56 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
57 SFE = 1, L/P = 2/5
58 lplus = 1, mplus = 1
59 [(-5,1;-1,2),2,0;?]
60
61 Modular symbol map (+)
62 (0:1) = {0,oo} -> -2/5
63 (1:1) = {0,1} -> 0
64 (2:1) = {0,1/2} -> -2
65 (3:1) = {0,1/3} -> -1
66 (4:1) = {0,1/4} -> 1
67 (5:1) = {0,1/5} -> 2
68 (6:1) = {0,1/6} -> 2
69 (7:1) = {0,1/7} -> 1
70 (8:1) = {0,1/8} -> -1
71 (9:1) = {0,1/9} -> -2
72 (10:1) = {0,1/10} -> 0
73 (1:0) = {oo,0} -> 2/5
74
75 Computation of further modular symbols
76
77 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
78 Enter numerator and denominator of r:
79 All modular symbols with bounded denominator
80
81 Enter maximum denominator (0 for none): {0,0} -> 0
82 {0,1/2} -> -2
83 {0,1/3} -> -1
84 {0,2/3} -> -1
85 {0,1/4} -> 1
86 {0,3/4} -> 1
87 {0,1/5} -> 2
88 {0,2/5} -> -3
89 {0,3/5} -> -3
90 {0,4/5} -> 2
91 >>> Level = conductor = 11 <<<
92 Minimal curve = [0,-1,1,-10,-20]
93
94 Enter sign (1,-1,0 for both):Newform information:
95
96 1 newform(s) at level 11:
97 p0=2
98 #ap= 100
99 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
100 aq = [ -1 ]
101 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
102 SFE = 1, L/P = 2/5
103 lplus = 1, mplus = 1
104 lminus = 3, mminus = -2
105 [(4,1;1,3),1,1;1]
106
107 Modular symbol map (+,-)
108 (0:1) = {0,oo} -> (-2/5,0)
109 (1:1) = {0,1} -> (0,0)
110 (2:1) = {0,1/2} -> (-2,0)
111 (3:1) = {0,1/3} -> (-1,-1)
112 (4:1) = {0,1/4} -> (1,-1)
113 (5:1) = {0,1/5} -> (2,0)
114 (6:1) = {0,1/6} -> (2,0)
115 (7:1) = {0,1/7} -> (1,1)
116 (8:1) = {0,1/8} -> (-1,1)
117 (9:1) = {0,1/9} -> (-2,0)
118 (10:1) = {0,1/10} -> (0,0)
119 (1:0) = {oo,0} -> (2/5,0)
120
121 Computation of further modular symbols
122
123 Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
124 Enter numerator and denominator of r:
125 All modular symbols with bounded denominator
126
127 Enter maximum denominator (0 for none): {oo,0} -> (2/5,0)
128 {oo,1/2} -> (-8/5,0)
129 {oo,1/3} -> (-3/5,-1)
130 {oo,2/3} -> (-3/5,1)
131 {oo,1/4} -> (7/5,-1)
132 {oo,3/4} -> (7/5,1)
133 {oo,1/5} -> (12/5,0)
134 {oo,2/5} -> (-13/5,-1)
135 {oo,3/5} -> (-13/5,1)
136 {oo,4/5} -> (12/5,0)
137 >>> Level = conductor = 11 <<<
138 Minimal curve = [0,-1,1,-10,-20]
139
140 Enter sign (1,-1,0 for both):Newform information:
141
142 1 newform(s) at level 11:
143 p0=2
144 #ap= 100
145 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
146 aq = [ -1 ]
147 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
148 SFE = 1, L/P = 2/5
149 lplus = 1, mplus = 1
150 [(-5,1;-1,2),2,0;?]
151
152 Modular symbol map (+)
153 (0:1) = {0,oo} -> -2/5
154 (1:1) = {0,1} -> 0
155 (2:1) = {0,1/2} -> -2
156 (3:1) = {0,1/3} -> -1
157 (4:1) = {0,1/4} -> 1
158 (5:1) = {0,1/5} -> 2
159 (6:1) = {0,1/6} -> 2
160 (7:1) = {0,1/7} -> 1
161 (8:1) = {0,1/8} -> -1
162 (9:1) = {0,1/9} -> -2
163 (10:1) = {0,1/10} -> 0
164 (1:0) = {oo,0} -> 2/5
165
166 Computation of further modular symbols
167
168 Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
169 Enter numerator and denominator of r:
170 All modular symbols with bounded denominator
171
172 Enter maximum denominator (0 for none): {oo,0} -> 2/5
173 {oo,1/2} -> -8/5
174 {oo,1/3} -> -3/5
175 {oo,2/3} -> -3/5
176 {oo,1/4} -> 7/5
177 {oo,3/4} -> 7/5
178 {oo,1/5} -> 12/5
179 {oo,2/5} -> -13/5
180 {oo,3/5} -> -13/5
181 {oo,4/5} -> 12/5
182 >>> Level = conductor = 11 <<<
183 Minimal curve = [0,-1,1,0,0]
184
185 Enter sign (1,-1,0 for both):Newform information:
186
187 1 newform(s) at level 11:
188 p0=2
189 #ap= 100
190 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
191 aq = [ -1 ]
192 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
193 SFE = 1, L/P = 2/5
194 lplus = 1, mplus = 1
195 lminus = 3, mminus = -2
196 [(4,1;1,3),1,1;1]
197
198 Modular symbol map (+,-)
199 (0:1) = {0,oo} -> (-2/25,0)
200 (1:1) = {0,1} -> (0,0)
201 (2:1) = {0,1/2} -> (-2/5,0)
202 (3:1) = {0,1/3} -> (-1/5,-1)
203 (4:1) = {0,1/4} -> (1/5,-1)
204 (5:1) = {0,1/5} -> (2/5,0)
205 (6:1) = {0,1/6} -> (2/5,0)
206 (7:1) = {0,1/7} -> (1/5,1)
207 (8:1) = {0,1/8} -> (-1/5,1)
208 (9:1) = {0,1/9} -> (-2/5,0)
209 (10:1) = {0,1/10} -> (0,0)
210 (1:0) = {oo,0} -> (2/25,0)
211
212 Computation of further modular symbols
213
214 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
215 Enter numerator and denominator of r:
216 All modular symbols with bounded denominator
217
218 Enter maximum denominator (0 for none): {0,0} -> (0,0)
219 {0,1/2} -> (-2/5,0)
220 {0,1/3} -> (-1/5,-1)
221 {0,2/3} -> (-1/5,1)
222 {0,1/4} -> (1/5,-1)
223 {0,3/4} -> (1/5,1)
224 {0,1/5} -> (2/5,0)
225 {0,2/5} -> (-3/5,-1)
226 {0,3/5} -> (-3/5,1)
227 {0,4/5} -> (2/5,0)
228 >>> Level = conductor = 11 <<<
229 Minimal curve = [0,-1,1,-7820,-263580]
230
231 Enter sign (1,-1,0 for both):Newform information:
232
233 1 newform(s) at level 11:
234 p0=2
235 #ap= 100
236 1: aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
237 aq = [ -1 ]
238 ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
239 SFE = 1, L/P = 2/5
240 lplus = 1, mplus = 1
241 lminus = 3, mminus = -2
242 [(4,1;1,3),1,1;1]
243
244 Modular symbol map (+,-)
245 (0:1) = {0,oo} -> (-2,0)
246 (1:1) = {0,1} -> (0,0)
247 (2:1) = {0,1/2} -> (-10,0)
248 (3:1) = {0,1/3} -> (-5,-1)
249 (4:1) = {0,1/4} -> (5,-1)
250 (5:1) = {0,1/5} -> (10,0)
251 (6:1) = {0,1/6} -> (10,0)
252 (7:1) = {0,1/7} -> (5,1)
253 (8:1) = {0,1/8} -> (-5,1)
254 (9:1) = {0,1/9} -> (-10,0)
255 (10:1) = {0,1/10} -> (0,0)
256 (1:0) = {oo,0} -> (2,0)
257
258 Computation of further modular symbols
259
260 Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
261 Enter numerator and denominator of r:
262 All modular symbols with bounded denominator
263
264 Enter maximum denominator (0 for none): {0,0} -> (0,0)
265 {0,1/2} -> (-10,0)
266 {0,1/3} -> (-5,-1)
267 {0,2/3} -> (-5,1)
268 {0,1/4} -> (5,-1)
269 {0,3/4} -> (5,1)
270 {0,1/5} -> (10,0)
271 {0,2/5} -> (-15,-1)
272 {0,3/5} -> (-15,1)
273 {0,4/5} -> (10,0)
274 >>> Level = conductor = 389 <<<
1275 Minimal curve = [0,1,1,-2,0]
2276
3277 Enter sign (1,-1,0 for both):Newform information:
13287 lminus = 3, mminus = -4
14288 [(-111,1;-2,7),1,1;2]
15289
16 Modular symbol map:
290 Modular symbol map (+,-)
17291 (0:1) = {0,oo} -> (0,0)
18292 (1:1) = {0,1} -> (0,0)
19293 (2:1) = {0,1/2} -> (0,0)