Atkin-Lehner |
2+ 7- 19+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
68894f |
Isogeny class |
Conductor |
68894 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
995328 |
Modular degree for the optimal curve |
Δ |
8105310206 = 2 · 78 · 19 · 37 |
Discriminant |
Eigenvalues |
2+ 2 3 7- -3 4 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2883626,-1885964002] |
[a1,a2,a3,a4,a6] |
Generators |
[606764775167120179690025:26697072990784745108140976:195493221014671109375] |
Generators of the group modulo torsion |
j |
22539927008317185433/68894 |
j-invariant |
L |
8.6930889172625 |
L(r)(E,1)/r! |
Ω |
0.11585500543022 |
Real period |
R |
37.517105475856 |
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 |
9842d1 |
Quadratic twists by: -7 |