Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ev |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
2231656650432 = 26 · 39 · 116 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11- -6 -8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3267,0] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:242:1] |
Generators of the group modulo torsion |
j |
1728 |
j-invariant |
L |
2.6760858944923 |
L(r)(E,1)/r! |
Ω |
0.69364128208583 |
Real period |
R |
1.9290128504471 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003752 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ev1 34848i2 69696et1 576g1 |
Quadratic twists by: -4 8 -3 -11 |