Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448bd |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-120777273274941504 = -1 · 26 · 34 · 1312 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 2 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-105512,21262710] |
[a1,a2,a3,a4,a6] |
j |
-420526439488/390971529 |
j-invariant |
L |
4.8371019029798 |
L(r)(E,1)/r! |
Ω |
0.30231886893647 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448d1 16224d2 97344ce1 2496o1 |
Quadratic twists by: -4 8 -3 13 |