Atkin-Lehner |
2- 5- 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
40480i |
Isogeny class |
Conductor |
40480 |
Conductor |
∏ cp |
52 |
Product of Tamagawa factors cp |
deg |
249600 |
Modular degree for the optimal curve |
Δ |
-13915000000000000 = -1 · 212 · 513 · 112 · 23 |
Discriminant |
Eigenvalues |
2- 0 5- -3 11+ -6 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-29672,-6006736] |
[a1,a2,a3,a4,a6] |
Generators |
[268:2300:1] [668:16500:1] |
Generators of the group modulo torsion |
j |
-705349276356096/3397216796875 |
j-invariant |
L |
8.4235026848341 |
L(r)(E,1)/r! |
Ω |
0.1645013549734 |
Real period |
R |
0.98473618210034 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40480e1 80960m1 |
Quadratic twists by: -4 8 |