Atkin-Lehner |
2- 3+ 11+ 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
31746x |
Isogeny class |
Conductor |
31746 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
-11189930524344 = -1 · 23 · 310 · 113 · 13 · 372 |
Discriminant |
Eigenvalues |
2- 3+ 3 1 11+ 13+ -8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-15479,752069] |
[a1,a2,a3,a4,a6] |
Generators |
[57:-272:1] |
Generators of the group modulo torsion |
j |
-410160814080220657/11189930524344 |
j-invariant |
L |
9.0121951670877 |
L(r)(E,1)/r! |
Ω |
0.71611386921657 |
Real period |
R |
1.0487386101677 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
95238bk1 |
Quadratic twists by: -3 |