Atkin-Lehner |
2+ 3- 23- |
Signs for the Atkin-Lehner involutions |
Class |
3312g |
Isogeny class |
Conductor |
3312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1536 |
Modular degree for the optimal curve |
Δ |
7243344 = 24 · 39 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -2 4 -4 -2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1866,-31025] |
[a1,a2,a3,a4,a6] |
Generators |
[311987:3520440:2197] |
Generators of the group modulo torsion |
j |
61604313088/621 |
j-invariant |
L |
3.3228706398956 |
L(r)(E,1)/r! |
Ω |
0.72639343004476 |
Real period |
R |
9.1489556553144 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1656a1 13248bo1 1104c1 82800bc1 |
Quadratic twists by: -4 8 -3 5 |