Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cx |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
817087626149363712 = 224 · 39 · 114 · 132 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 11+ 13- 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8635612716,-308878620735024] |
[a1,a2,a3,a4,a6] |
Generators |
[308038172363665695124814226109410966:262577690733630829381195505870512048896:416903268970582627641051479471] |
Generators of the group modulo torsion |
j |
13802951728468271053322091/158357056 |
j-invariant |
L |
6.6406002940154 |
L(r)(E,1)/r! |
Ω |
0.01566124434352 |
Real period |
R |
53.001857230799 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368o2 20592w2 82368dh2 |
Quadratic twists by: -4 8 -3 |