Atkin-Lehner |
2+ 3- 5+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
42840i |
Isogeny class |
Conductor |
42840 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
89592095250000 = 24 · 311 · 56 · 7 · 172 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -2 0 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11478,128977] |
[a1,a2,a3,a4,a6] |
Generators |
[-91:648:1] [-52:765:1] |
Generators of the group modulo torsion |
j |
14337547257856/7681078125 |
j-invariant |
L |
8.5453982281929 |
L(r)(E,1)/r! |
Ω |
0.52808081230614 |
Real period |
R |
2.0227487036679 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85680y1 14280bx1 |
Quadratic twists by: -4 -3 |