Atkin-Lehner |
2+ 5+ 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
8710c |
Isogeny class |
Conductor |
8710 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1152 |
Modular degree for the optimal curve |
Δ |
278720 = 26 · 5 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 0 5+ -3 -2 13+ 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-35,85] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:14:1] [-2:13:1] |
Generators of the group modulo torsion |
j |
4818245769/278720 |
j-invariant |
L |
3.8806694391625 |
L(r)(E,1)/r! |
Ω |
3.0411763290338 |
Real period |
R |
0.63802111737385 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69680n1 78390ca1 43550u1 113230s1 |
Quadratic twists by: -4 -3 5 13 |