Atkin-Lehner |
2+ 5- 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
8710f |
Isogeny class |
Conductor |
8710 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
14400 |
Modular degree for the optimal curve |
Δ |
29439800000 = 26 · 55 · 133 · 67 |
Discriminant |
Eigenvalues |
2+ 0 5- 1 -2 13+ 6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-36494,2692500] |
[a1,a2,a3,a4,a6] |
Generators |
[116:42:1] |
Generators of the group modulo torsion |
j |
5375202242262578361/29439800000 |
j-invariant |
L |
3.2992765390892 |
L(r)(E,1)/r! |
Ω |
1.0457702959655 |
Real period |
R |
0.31548768900949 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69680x1 78390bo1 43550t1 113230m1 |
Quadratic twists by: -4 -3 5 13 |