Atkin-Lehner |
2- 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
2232j |
Isogeny class |
Conductor |
2232 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-361584 = -1 · 24 · 36 · 31 |
Discriminant |
Eigenvalues |
2- 3- -1 -3 2 -2 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3,-29] |
[a1,a2,a3,a4,a6] |
Generators |
[5:9:1] |
Generators of the group modulo torsion |
j |
-256/31 |
j-invariant |
L |
2.8116690333249 |
L(r)(E,1)/r! |
Ω |
1.3408616956504 |
Real period |
R |
0.52422800995167 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4464h1 17856l1 248a1 55800o1 |
Quadratic twists by: -4 8 -3 5 |