Atkin-Lehner |
2+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
32032b |
Isogeny class |
Conductor |
32032 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
165120 |
Modular degree for the optimal curve |
Δ |
-1585439270711296 = -1 · 212 · 75 · 116 · 13 |
Discriminant |
Eigenvalues |
2+ 2 -3 7+ 11+ 13- 2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2723,-1915851] |
[a1,a2,a3,a4,a6] |
j |
544938117632/387070134451 |
j-invariant |
L |
0.88748585335524 |
L(r)(E,1)/r! |
Ω |
0.22187146334025 |
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 |
32032n1 64064g1 |
Quadratic twists by: -4 8 |