Atkin-Lehner |
2+ 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696be |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
429229228032 = 214 · 39 · 113 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 11+ -4 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3036,56144] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:288:1] [-11:297:1] |
Generators of the group modulo torsion |
j |
194672/27 |
j-invariant |
L |
8.7150701058547 |
L(r)(E,1)/r! |
Ω |
0.90594171546489 |
Real period |
R |
1.2024876927942 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999675 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ff1 8712e1 23232d1 69696bd1 |
Quadratic twists by: -4 8 -3 -11 |