Atkin-Lehner |
2+ 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696j |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
6284345127616512 = 214 · 39 · 117 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 11- -6 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-65340,5174928] |
[a1,a2,a3,a4,a6] |
Generators |
[36630:-418176:125] [-194:3248:1] |
Generators of the group modulo torsion |
j |
54000/11 |
j-invariant |
L |
10.823299426409 |
L(r)(E,1)/r! |
Ω |
0.40119157450083 |
Real period |
R |
3.3722353964836 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999881 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696eh1 8712q1 69696i1 6336i1 |
Quadratic twists by: -4 8 -3 -11 |