Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984u |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-541991420192772864 = -1 · 28 · 38 · 199 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 -5 2 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,177612,-20604436] |
[a1,a2,a3,a4,a6] |
Generators |
[49609:11049849:1] |
Generators of the group modulo torsion |
j |
70575104/61731 |
j-invariant |
L |
5.872923836835 |
L(r)(E,1)/r! |
Ω |
0.16083092259612 |
Real period |
R |
4.5645169955469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992bb1 17328e1 2736f1 |
Quadratic twists by: -4 -3 -19 |