Atkin-Lehner |
2+ 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368h |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
599501979648 = 214 · 39 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -2 11+ 13- -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-67068,6685200] |
[a1,a2,a3,a4,a6] |
j |
103456682352/1859 |
j-invariant |
L |
3.3683325490634 |
L(r)(E,1)/r! |
Ω |
0.84208313286454 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368di1 10296h1 82368p1 |
Quadratic twists by: -4 8 -3 |