Atkin-Lehner |
2- 3+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12144z |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
386792423424 = 221 · 36 · 11 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -3 1 11- -7 -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2032,-17984] |
[a1,a2,a3,a4,a6] |
Generators |
[-38:54:1] [-24:128:1] |
Generators of the group modulo torsion |
j |
226646274673/94431744 |
j-invariant |
L |
4.9333282655081 |
L(r)(E,1)/r! |
Ω |
0.73779966428165 |
Real period |
R |
0.83581771996185 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1518p1 48576df1 36432bm1 |
Quadratic twists by: -4 8 -3 |