Atkin-Lehner |
2+ 3+ 5+ 7+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
8610a |
Isogeny class |
Conductor |
8610 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
86519150298000 = 24 · 37 · 53 · 7 · 414 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -4 -2 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-42108,-3313152] |
[a1,a2,a3,a4,a6] |
Generators |
[1028:31752:1] |
Generators of the group modulo torsion |
j |
8257216470354032329/86519150298000 |
j-invariant |
L |
2.1181539953676 |
L(r)(E,1)/r! |
Ω |
0.3334893119639 |
Real period |
R |
6.3514898960145 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68880cg1 25830bf1 43050by1 60270o1 |
Quadratic twists by: -4 -3 5 -7 |