Atkin-Lehner |
3- 7- 19- 31- |
Signs for the Atkin-Lehner involutions |
Class |
12369k |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
6444459273 = 3 · 76 · 19 · 312 |
Discriminant |
Eigenvalues |
1 3- 0 7- -2 0 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1256,16577] |
[a1,a2,a3,a4,a6] |
Generators |
[310:1143:8] |
Generators of the group modulo torsion |
j |
218874659109625/6444459273 |
j-invariant |
L |
6.6766935077333 |
L(r)(E,1)/r! |
Ω |
1.3312995929939 |
Real period |
R |
1.671723265214 |
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 |
37107p1 86583d1 |
Quadratic twists by: -3 -7 |