Atkin-Lehner |
2- 3- 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
12078x |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
217728 |
Modular degree for the optimal curve |
Δ |
-450276280293512376 = -1 · 23 · 327 · 112 · 61 |
Discriminant |
Eigenvalues |
2- 3- -3 -4 11- 2 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,9841,-32285041] |
[a1,a2,a3,a4,a6] |
Generators |
[6561:528160:1] |
Generators of the group modulo torsion |
j |
144595657865303/617662935930744 |
j-invariant |
L |
4.9155321625093 |
L(r)(E,1)/r! |
Ω |
0.1374566298851 |
Real period |
R |
1.4900251830396 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96624bn1 4026c1 |
Quadratic twists by: -4 -3 |