Atkin-Lehner |
2+ 3- 13- |
Signs for the Atkin-Lehner involutions |
Class |
32448bt |
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 |
[199:2808:1] |
Generators of the group modulo torsion |
j |
256000/9 |
j-invariant |
L |
7.4034057772892 |
L(r)(E,1)/r! |
Ω |
1.3186095574184 |
Real period |
R |
2.8072774596688 |
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 |
32448ct1 4056o1 97344da1 32448bu1 |
Quadratic twists by: -4 8 -3 13 |