Atkin-Lehner |
2+ 3+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744g |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
401783570496 = 26 · 32 · 78 · 112 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11+ 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7562,253800] |
[a1,a2,a3,a4,a6] |
j |
6352182208/53361 |
j-invariant |
L |
1.9045123076602 |
L(r)(E,1)/r! |
Ω |
0.95225615424134 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51744cm1 103488ea2 7392f1 |
Quadratic twists by: -4 8 -7 |