Atkin-Lehner |
2- 3+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
32208k |
Isogeny class |
Conductor |
32208 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1399680 |
Modular degree for the optimal curve |
Δ |
-8921484864805404672 = -1 · 222 · 39 · 116 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 4 -4 11- 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,173064,-141067152] |
[a1,a2,a3,a4,a6] |
Generators |
[115158940:617940224:274625] |
Generators of the group modulo torsion |
j |
139952759660884871/2178096890821632 |
j-invariant |
L |
5.9395015976762 |
L(r)(E,1)/r! |
Ω |
0.11305395326284 |
Real period |
R |
8.7561461087923 |
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 |
4026b1 128832bl1 96624bj1 |
Quadratic twists by: -4 8 -3 |