Atkin-Lehner |
2- 3+ 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
32208l |
Isogeny class |
Conductor |
32208 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
127872 |
Modular degree for the optimal curve |
Δ |
-213982786879488 = -1 · 230 · 33 · 112 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11- 2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-29488,-2062400] |
[a1,a2,a3,a4,a6] |
j |
-692332063944625/52241891328 |
j-invariant |
L |
3.2647576749321 |
L(r)(E,1)/r! |
Ω |
0.18137542638521 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4026i1 128832bi1 96624bk1 |
Quadratic twists by: -4 8 -3 |