Atkin-Lehner |
2- 3- 7- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
57288s |
Isogeny class |
Conductor |
57288 |
Conductor |
∏ cp |
204 |
Product of Tamagawa factors cp |
deg |
502656 |
Modular degree for the optimal curve |
Δ |
-7491891958944624 = -1 · 24 · 317 · 73 · 11 · 312 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 11+ -1 -2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-765616,257627093] |
[a1,a2,a3,a4,a6] |
Generators |
[554:1953:1] |
Generators of the group modulo torsion |
j |
-3101967899504959500544/468243247434039 |
j-invariant |
L |
6.7532024885508 |
L(r)(E,1)/r! |
Ω |
0.40345058914767 |
Real period |
R |
0.082052014936905 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000108 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
114576d1 |
Quadratic twists by: -4 |