Atkin-Lehner |
2+ 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69192d |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
892800 |
Modular degree for the optimal curve |
Δ |
159169936971389184 = 28 · 36 · 318 |
Discriminant |
Eigenvalues |
2+ 3- 1 -3 1 -5 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1698087,851486362] |
[a1,a2,a3,a4,a6] |
j |
3402064 |
j-invariant |
L |
0.63314878789036 |
L(r)(E,1)/r! |
Ω |
0.31657439767135 |
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 |
7688d1 69192i1 |
Quadratic twists by: -3 -31 |