Atkin-Lehner |
2- 3+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
32448cs |
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 |
[-83:1932:1] |
Generators of the group modulo torsion |
j |
256000/9 |
j-invariant |
L |
4.9586202326844 |
L(r)(E,1)/r! |
Ω |
0.59538181019113 |
Real period |
R |
4.1642355777485 |
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 |
32448bu1 8112r1 97344gf1 32448ct1 |
Quadratic twists by: -4 8 -3 13 |