Atkin-Lehner |
2- 3+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
32448ct |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
20247552 = 210 · 32 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 2 13- -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-173,909] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:39:1] |
Generators of the group modulo torsion |
j |
256000/9 |
j-invariant |
L |
3.9678021671268 |
L(r)(E,1)/r! |
Ω |
2.1466796451227 |
Real period |
R |
0.92417193598072 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448bt1 8112s1 97344gg1 32448cs1 |
Quadratic twists by: -4 8 -3 13 |