Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828b |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
58556160 |
Modular degree for the optimal curve |
Δ |
-5.5496483468902E+29 |
Discriminant |
Eigenvalues |
2- 3+ 0 3 11+ 1 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-184776173,-35854860511095] |
[a1,a2,a3,a4,a6] |
Generators |
[104159942133659493268690691340104826998683137396181715232:30305445362738362268346605963957258429611294293813796486263:1144459437542359953842990795605240222201203763417619] |
Generators of the group modulo torsion |
j |
-34801580274688000/27682340832837603 |
j-invariant |
L |
6.3901628188485 |
L(r)(E,1)/r! |
Ω |
0.013142072924778 |
Real period |
R |
81.039508954995 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69828k1 |
Quadratic twists by: -23 |