Atkin-Lehner |
2- 3+ 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
12408c |
Isogeny class |
Conductor |
12408 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
33030096 = 24 · 3 · 114 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 2 0 11+ -6 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-87,-120] |
[a1,a2,a3,a4,a6] |
Generators |
[17:55:1] |
Generators of the group modulo torsion |
j |
4604090368/2064381 |
j-invariant |
L |
4.4254510905075 |
L(r)(E,1)/r! |
Ω |
1.6285154571836 |
Real period |
R |
2.7174756438364 |
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 |
24816f1 99264y1 37224f1 |
Quadratic twists by: -4 8 -3 |