Atkin-Lehner |
2- 3+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
8112y |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-34987769856 = -1 · 216 · 35 · 133 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 0 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,776,3184] |
[a1,a2,a3,a4,a6] |
Generators |
[9:104:1] |
Generators of the group modulo torsion |
j |
5735339/3888 |
j-invariant |
L |
3.3060862324447 |
L(r)(E,1)/r! |
Ω |
0.73119009001888 |
Real period |
R |
2.2607570025733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1014c1 32448di1 24336cc1 8112w1 |
Quadratic twists by: -4 8 -3 13 |