Atkin-Lehner |
2+ 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368f |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
6782976 |
Modular degree for the optimal curve |
Δ |
-8.0788299652314E+19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 11+ 13- -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59969484,-178749506960] |
[a1,a2,a3,a4,a6] |
j |
-3369853043629824680811/11414181695488 |
j-invariant |
L |
0.10850430030145 |
L(r)(E,1)/r! |
Ω |
0.027126070912728 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dh1 2574b1 82368o1 |
Quadratic twists by: -4 8 -3 |