Atkin-Lehner |
3- 13+ 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12597c |
Isogeny class |
Conductor |
12597 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
19200 |
Modular degree for the optimal curve |
Δ |
973846218033 = 32 · 132 · 173 · 194 |
Discriminant |
Eigenvalues |
1 3- 0 2 6 13+ 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2486,-4741] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:220:1] |
Generators of the group modulo torsion |
j |
1698149553297625/973846218033 |
j-invariant |
L |
7.4685316157177 |
L(r)(E,1)/r! |
Ω |
0.73383316344226 |
Real period |
R |
1.6962374164822 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37791c1 |
Quadratic twists by: -3 |