Atkin-Lehner |
2+ 7+ 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
85358a |
Isogeny class |
Conductor |
85358 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
312480 |
Modular degree for the optimal curve |
Δ |
-40169133368 = -1 · 23 · 78 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 3 0 7+ 0 13+ -3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-22402,-1285012] |
[a1,a2,a3,a4,a6] |
j |
-215680397625/6968 |
j-invariant |
L |
3.1218791131654 |
L(r)(E,1)/r! |
Ω |
0.19511744941613 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85358l1 |
Quadratic twists by: -7 |