Atkin-Lehner |
3+ 13+ 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
51129b |
Isogeny class |
Conductor |
51129 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
388800 |
Modular degree for the optimal curve |
Δ |
-2462732207913627 = -1 · 39 · 133 · 195 · 23 |
Discriminant |
Eigenvalues |
-1 3+ 4 -3 -4 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-28298,3016684] |
[a1,a2,a3,a4,a6] |
j |
-127316666284443/125119758569 |
j-invariant |
L |
0.83478645871001 |
L(r)(E,1)/r! |
Ω |
0.41739322949578 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51129a1 |
Quadratic twists by: -3 |