Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ef |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
267028634668105728 = 222 · 33 · 119 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 11- 2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-675180,212086864] |
[a1,a2,a3,a4,a6] |
Generators |
[3740:223608:1] |
Generators of the group modulo torsion |
j |
2714704875/21296 |
j-invariant |
L |
6.9379994222479 |
L(r)(E,1)/r! |
Ω |
0.31160256776831 |
Real period |
R |
2.7831924941855 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999921 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696l1 17424bd1 69696ee3 6336bp1 |
Quadratic twists by: -4 8 -3 -11 |