Atkin-Lehner |
2+ 3+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192c |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
698368 |
Modular degree for the optimal curve |
Δ |
-1462005346996463616 = -1 · 211 · 33 · 319 |
Discriminant |
Eigenvalues |
2+ 3+ 1 2 -3 1 1 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,89373,57258302] |
[a1,a2,a3,a4,a6] |
j |
54 |
j-invariant |
L |
3.210826203788 |
L(r)(E,1)/r! |
Ω |
0.20067663781194 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69192bb1 69192b1 |
Quadratic twists by: -3 -31 |