Atkin-Lehner |
2- 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368et |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
599040 |
Modular degree for the optimal curve |
Δ |
-2462556006383616 = -1 · 231 · 36 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- -3 5 11- 13+ -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,7476,2374544] |
[a1,a2,a3,a4,a6] |
j |
241804367/12886016 |
j-invariant |
L |
1.3930790564146 |
L(r)(E,1)/r! |
Ω |
0.34826977573225 |
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 |
82368ba1 20592bi1 9152q1 |
Quadratic twists by: -4 8 -3 |