Atkin-Lehner |
2+ 31- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85312i |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
11450382811136 = 233 · 31 · 43 |
Discriminant |
Eigenvalues |
2+ 2 3 -4 3 7 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-24769,1499841] |
[a1,a2,a3,a4,a6] |
j |
6411014266033/43679744 |
j-invariant |
L |
5.7643181670262 |
L(r)(E,1)/r! |
Ω |
0.7205397897974 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312r1 2666e1 |
Quadratic twists by: -4 8 |