Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966m |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-283613674731409152 = -1 · 28 · 310 · 138 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 0 2 2 13+ 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-46422,-25898508] |
[a1,a2,a3,a4,a6] |
Generators |
[26484:310731:64] |
Generators of the group modulo torsion |
j |
-3144219625/80600832 |
j-invariant |
L |
5.9344277847426 |
L(r)(E,1)/r! |
Ω |
0.13369266738844 |
Real period |
R |
5.5485726143283 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001144 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322s1 5382o1 |
Quadratic twists by: -3 13 |