Atkin-Lehner |
2+ 3+ 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264b |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
75264 |
Modular degree for the optimal curve |
Δ |
-4551475968 = -1 · 28 · 33 · 13 · 373 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 1 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7596,-254836] |
[a1,a2,a3,a4,a6] |
j |
-7012531915776/658489 |
j-invariant |
L |
1.5341651946348 |
L(r)(E,1)/r! |
Ω |
0.25569419787852 |
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 |
34632a1 69264a1 |
Quadratic twists by: -4 -3 |