Atkin-Lehner |
2+ 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368z |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-159375295512576 = -1 · 221 · 312 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -3 5 11+ 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,7476,554096] |
[a1,a2,a3,a4,a6] |
j |
241804367/833976 |
j-invariant |
L |
1.6318463180923 |
L(r)(E,1)/r! |
Ω |
0.40796157286365 |
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 |
82368eu1 2574o1 27456r1 |
Quadratic twists by: -4 8 -3 |