Atkin-Lehner |
2+ 3- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31248r |
Isogeny class |
Conductor |
31248 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
3280290048 = 28 · 310 · 7 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 0 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-759,-7562] |
[a1,a2,a3,a4,a6] |
Generators |
[81:680:1] |
Generators of the group modulo torsion |
j |
259108432/17577 |
j-invariant |
L |
7.085954025539 |
L(r)(E,1)/r! |
Ω |
0.91345673950237 |
Real period |
R |
3.8786478434651 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15624j1 124992fz1 10416k1 |
Quadratic twists by: -4 8 -3 |