Atkin-Lehner |
2- 7+ 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
32396a |
Isogeny class |
Conductor |
32396 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
14016 |
Modular degree for the optimal curve |
Δ |
-188674304 = -1 · 28 · 72 · 132 · 89 |
Discriminant |
Eigenvalues |
2- -1 3 7+ -6 13- -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-124,-808] |
[a1,a2,a3,a4,a6] |
Generators |
[34:-182:1] |
Generators of the group modulo torsion |
j |
-830321872/737009 |
j-invariant |
L |
4.3723585092013 |
L(r)(E,1)/r! |
Ω |
0.6893647200268 |
Real period |
R |
0.52854925486458 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129584r1 |
Quadratic twists by: -4 |