Atkin-Lehner |
2- 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448cd |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
479232 |
Modular degree for the optimal curve |
Δ |
-5203983814166052864 = -1 · 222 · 32 · 1310 |
Discriminant |
Eigenvalues |
2- 3+ -1 -2 -2 13+ 5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-38081,109805409] |
[a1,a2,a3,a4,a6] |
j |
-169/144 |
j-invariant |
L |
0.78206695556502 |
L(r)(E,1)/r! |
Ω |
0.19551673889045 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32448z1 8112bb1 97344eu1 32448ca1 |
Quadratic twists by: -4 8 -3 13 |