Atkin-Lehner |
2- 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
12272i |
Isogeny class |
Conductor |
12272 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-2613837824 = -1 · 218 · 132 · 59 |
Discriminant |
Eigenvalues |
2- 3 -1 5 0 13- -6 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,77,-2446] |
[a1,a2,a3,a4,a6] |
j |
12326391/638144 |
j-invariant |
L |
5.5181767242223 |
L(r)(E,1)/r! |
Ω |
0.68977209052779 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1534b1 49088p1 110448bn1 |
Quadratic twists by: -4 8 -3 |