Atkin-Lehner |
2- 5+ 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
8540b |
Isogeny class |
Conductor |
8540 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
29760 |
Modular degree for the optimal curve |
Δ |
9116450000 = 24 · 55 · 72 · 612 |
Discriminant |
Eigenvalues |
2- 2 5+ 7+ 4 -6 8 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-51021,-4418830] |
[a1,a2,a3,a4,a6] |
Generators |
[-5508973434110:-7427029218:42326109125] |
Generators of the group modulo torsion |
j |
918034792531492864/569778125 |
j-invariant |
L |
5.5257244941845 |
L(r)(E,1)/r! |
Ω |
0.31765933317908 |
Real period |
R |
17.395127159917 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34160x1 76860k1 42700m1 59780m1 |
Quadratic twists by: -4 -3 5 -7 |