Atkin-Lehner |
2+ 3+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192b |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
22528 |
Modular degree for the optimal curve |
Δ |
-1647323136 = -1 · 211 · 33 · 313 |
Discriminant |
Eigenvalues |
2+ 3+ 1 2 3 -1 -1 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,93,-1922] |
[a1,a2,a3,a4,a6] |
j |
54 |
j-invariant |
L |
2.917051528968 |
L(r)(E,1)/r! |
Ω |
0.72926287907939 |
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 |
69192bc1 69192c1 |
Quadratic twists by: -3 -31 |