Atkin-Lehner |
2+ 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368o |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
20348928 |
Modular degree for the optimal curve |
Δ |
-5.8894670446537E+22 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 11- 13- 8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-539725356,4826236687920] |
[a1,a2,a3,a4,a6] |
Generators |
[-4298:2658304:1] |
Generators of the group modulo torsion |
j |
-3369853043629824680811/11414181695488 |
j-invariant |
L |
5.782943496517 |
L(r)(E,1)/r! |
Ω |
0.097226369359393 |
Real period |
R |
3.717447958676 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006302 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cx1 2574q1 82368f1 |
Quadratic twists by: -4 8 -3 |