Atkin-Lehner |
2+ 5- 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
8710h |
Isogeny class |
Conductor |
8710 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
10368 |
Modular degree for the optimal curve |
Δ |
6804687500 = 22 · 59 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ -2 5- -1 -6 13- 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1528,22506] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:209:1] [-20:222:1] |
Generators of the group modulo torsion |
j |
394171426055161/6804687500 |
j-invariant |
L |
3.3344927153132 |
L(r)(E,1)/r! |
Ω |
1.3327484290506 |
Real period |
R |
1.250983547468 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
69680be1 78390bs1 43550p1 113230q1 |
Quadratic twists by: -4 -3 5 13 |