Atkin-Lehner |
2+ 5- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
15730m |
Isogeny class |
Conductor |
15730 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
362880 |
Modular degree for the optimal curve |
Δ |
121481128912000000 = 210 · 56 · 112 · 137 |
Discriminant |
Eigenvalues |
2+ -1 5- -4 11- 13+ -1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1573332,-760059824] |
[a1,a2,a3,a4,a6] |
Generators |
[-728:764:1] |
Generators of the group modulo torsion |
j |
3559589366328163617361/1003976272000000 |
j-invariant |
L |
2.2997714426229 |
L(r)(E,1)/r! |
Ω |
0.13480368852225 |
Real period |
R |
1.4216793495747 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
125840ch1 78650ch1 15730bc1 |
Quadratic twists by: -4 5 -11 |