Atkin-Lehner |
2+ 3- 13- |
Signs for the Atkin-Lehner involutions |
Class |
32448bu |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
79872 |
Modular degree for the optimal curve |
Δ |
97731066221568 = 210 · 32 · 139 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 2 13- -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-29293,-1879981] |
[a1,a2,a3,a4,a6] |
Generators |
[-84910:48177:1000] |
Generators of the group modulo torsion |
j |
256000/9 |
j-invariant |
L |
6.2529292157013 |
L(r)(E,1)/r! |
Ω |
0.36571649012223 |
Real period |
R |
8.5488751322253 |
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 |
32448cs1 4056e1 97344db1 32448bt1 |
Quadratic twists by: -4 8 -3 13 |