Atkin-Lehner |
2+ 7- 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
57722i |
Isogeny class |
Conductor |
57722 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
399360 |
Modular degree for the optimal curve |
Δ |
-67647714614050816 = -1 · 220 · 78 · 192 · 31 |
Discriminant |
Eigenvalues |
2+ 0 -2 7- 2 4 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-105653,18228405] |
[a1,a2,a3,a4,a6] |
Generators |
[51:3576:1] |
Generators of the group modulo torsion |
j |
-1108621467544473/574996086784 |
j-invariant |
L |
3.866931817734 |
L(r)(E,1)/r! |
Ω |
0.32348985065365 |
Real period |
R |
2.9884491041682 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000415 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8246a1 |
Quadratic twists by: -7 |