Atkin-Lehner |
2- 7+ 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
57134p |
Isogeny class |
Conductor |
57134 |
Conductor |
∏ cp |
414 |
Product of Tamagawa factors cp |
deg |
1145952 |
Modular degree for the optimal curve |
Δ |
75302926582546432 = 223 · 74 · 113 · 532 |
Discriminant |
Eigenvalues |
2- -1 -2 7+ 11- -1 -4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3217929,2220460087] |
[a1,a2,a3,a4,a6] |
Generators |
[-785:65688:1] |
Generators of the group modulo torsion |
j |
1534832311490255611057/31363151429632 |
j-invariant |
L |
5.9622855663715 |
L(r)(E,1)/r! |
Ω |
0.31764900380911 |
Real period |
R |
0.045338268922152 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999082 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57134u1 |
Quadratic twists by: -7 |