Atkin-Lehner |
2+ 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12480f |
Isogeny class |
Conductor |
12480 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
14325948748800 = 210 · 316 · 52 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 4 0 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9181,-282419] |
[a1,a2,a3,a4,a6] |
Generators |
[-60:221:1] |
Generators of the group modulo torsion |
j |
83587439220736/13990184325 |
j-invariant |
L |
4.298207568141 |
L(r)(E,1)/r! |
Ω |
0.49327341407408 |
Real period |
R |
4.3568206247331 |
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 |
12480cp1 1560h1 37440cj1 62400de1 |
Quadratic twists by: -4 8 -3 5 |