Atkin-Lehner |
2+ 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12480a |
Isogeny class |
Conductor |
12480 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
1380188160 = 218 · 34 · 5 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 13+ 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7041,229761] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:576:1] |
Generators of the group modulo torsion |
j |
147281603041/5265 |
j-invariant |
L |
3.4058133531174 |
L(r)(E,1)/r! |
Ω |
1.4222917416163 |
Real period |
R |
1.1972977320557 |
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 |
12480cj1 195a1 37440ca1 62400cs1 |
Quadratic twists by: -4 8 -3 5 |