Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
123786h |
Isogeny class |
Conductor |
123786 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
995328 |
Modular degree for the optimal curve |
Δ |
2155086991429632 = 212 · 39 · 133 · 233 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 -6 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-251397,48527829] |
[a1,a2,a3,a4,a6] |
Generators |
[75:5448:1] |
Generators of the group modulo torsion |
j |
198104308022375/242970624 |
j-invariant |
L |
2.9720330383408 |
L(r)(E,1)/r! |
Ω |
0.46188522172715 |
Real period |
R |
3.2172853194855 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998386312 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
41262v1 123786g1 |
Quadratic twists by: -3 -23 |