Atkin-Lehner |
2- 3+ 5- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
34320bn |
Isogeny class |
Conductor |
34320 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
33165737459712000 = 236 · 33 · 53 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 5- 4 11- 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-182720,28818432] |
[a1,a2,a3,a4,a6] |
Generators |
[337:2324:1] |
Generators of the group modulo torsion |
j |
164711681450297281/8097103872000 |
j-invariant |
L |
6.2975139542369 |
L(r)(E,1)/r! |
Ω |
0.36430912243031 |
Real period |
R |
5.7620608127387 |
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 |
4290bb1 102960dj1 |
Quadratic twists by: -4 -3 |