Atkin-Lehner |
2- 3- 7+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31122z |
Isogeny class |
Conductor |
31122 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
1193011202948292 = 22 · 37 · 76 · 132 · 193 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ -2 13- -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-649976,-201525033] |
[a1,a2,a3,a4,a6] |
j |
41656954888931716153/1636503707748 |
j-invariant |
L |
0.67256814163093 |
L(r)(E,1)/r! |
Ω |
0.1681420354074 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10374b1 |
Quadratic twists by: -3 |