Atkin-Lehner |
2- 3- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
3312m |
Isogeny class |
Conductor |
3312 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
240 |
Modular degree for the optimal curve |
Δ |
-268272 = -1 · 24 · 36 · 23 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 0 -1 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,15,11] |
[a1,a2,a3,a4,a6] |
Generators |
[2:7:1] |
Generators of the group modulo torsion |
j |
32000/23 |
j-invariant |
L |
3.3045985332053 |
L(r)(E,1)/r! |
Ω |
1.9689909900092 |
Real period |
R |
1.6783207998275 |
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 |
828d1 13248bc1 368e1 82800ed1 |
Quadratic twists by: -4 8 -3 5 |