Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368fa |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-3200841840328704 = -1 · 221 · 36 · 115 · 13 |
Discriminant |
Eigenvalues |
2- 3- -1 -1 11- 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-38028,-3944176] |
[a1,a2,a3,a4,a6] |
Generators |
[460:8712:1] |
Generators of the group modulo torsion |
j |
-31824875809/16749304 |
j-invariant |
L |
5.6549630891121 |
L(r)(E,1)/r! |
Ω |
0.16681744186043 |
Real period |
R |
1.6949555825947 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000354 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368bf1 20592ba1 9152w1 |
Quadratic twists by: -4 8 -3 |