Atkin-Lehner |
2- 3+ 7+ 11+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
33726k |
Isogeny class |
Conductor |
33726 |
Conductor |
∏ cp |
176 |
Product of Tamagawa factors cp |
deg |
87296 |
Modular degree for the optimal curve |
Δ |
16338294669312 = 222 · 32 · 72 · 112 · 73 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11+ 0 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-6969,-113913] |
[a1,a2,a3,a4,a6] |
Generators |
[175:-2104:1] [-65:296:1] |
Generators of the group modulo torsion |
j |
37431652514343697/16338294669312 |
j-invariant |
L |
9.550721192699 |
L(r)(E,1)/r! |
Ω |
0.54381554441568 |
Real period |
R |
0.39914608458253 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
101178r1 |
Quadratic twists by: -3 |