Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cm |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
-6350280228864 = -1 · 215 · 36 · 112 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 3 -1 11- 13- 5 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5196,-188368] |
[a1,a2,a3,a4,a6] |
j |
-649461896/265837 |
j-invariant |
L |
3.3074030959052 |
L(r)(E,1)/r! |
Ω |
0.27561691885327 |
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 |
82368bk1 41184j1 9152f1 |
Quadratic twists by: -4 8 -3 |