Atkin-Lehner |
2+ 3- 5+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
118440x |
Isogeny class |
Conductor |
118440 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
399360 |
Modular degree for the optimal curve |
Δ |
-30590721811440 = -1 · 24 · 319 · 5 · 7 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -1 -2 -8 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-48963,-4178617] |
[a1,a2,a3,a4,a6] |
Generators |
[571:12411:1] [1042:32805:1] |
Generators of the group modulo torsion |
j |
-1112961803305216/2622661335 |
j-invariant |
L |
11.622231942233 |
L(r)(E,1)/r! |
Ω |
0.16045056155525 |
Real period |
R |
9.0543715082846 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999982449 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39480w1 |
Quadratic twists by: -3 |