Atkin-Lehner |
2- 5+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
68770n |
Isogeny class |
Conductor |
68770 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
1689600 |
Modular degree for the optimal curve |
Δ |
141640738595200000 = 210 · 55 · 13 · 237 |
Discriminant |
Eigenvalues |
2- -3 5+ 1 4 13+ -7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-133143,4701231] |
[a1,a2,a3,a4,a6] |
Generators |
[-109:4286:1] |
Generators of the group modulo torsion |
j |
1763228727441/956800000 |
j-invariant |
L |
5.5000399351524 |
L(r)(E,1)/r! |
Ω |
0.28500832281658 |
Real period |
R |
0.48244555471401 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985058 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2990g1 |
Quadratic twists by: -23 |