Atkin-Lehner |
2- 7+ 11+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
50512d |
Isogeny class |
Conductor |
50512 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
5289501139664896 = 219 · 75 · 114 · 41 |
Discriminant |
Eigenvalues |
2- 1 -1 7+ 11+ -2 -5 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-241176,45373076] |
[a1,a2,a3,a4,a6] |
Generators |
[-458:7744:1] [268:242:1] |
Generators of the group modulo torsion |
j |
378763245046164889/1291382114176 |
j-invariant |
L |
10.060417852222 |
L(r)(E,1)/r! |
Ω |
0.43164525581271 |
Real period |
R |
2.9133929183586 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6314f1 |
Quadratic twists by: -4 |