Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dt |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-3607259774976 = -1 · 220 · 37 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 -4 11+ 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3756,-127280] |
[a1,a2,a3,a4,a6] |
Generators |
[138:1408:1] |
Generators of the group modulo torsion |
j |
-30664297/18876 |
j-invariant |
L |
3.2581573356833 |
L(r)(E,1)/r! |
Ω |
0.29661835541584 |
Real period |
R |
2.746085395739 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000065 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bx1 20592bv1 27456cf1 |
Quadratic twists by: -4 8 -3 |