Atkin-Lehner |
2+ 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368bh |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
39288961738211328 = 230 · 39 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 11+ 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-614604,-185210768] |
[a1,a2,a3,a4,a6] |
Generators |
[338506221526:-9623946608640:248858189] |
Generators of the group modulo torsion |
j |
134351465835313/205590528 |
j-invariant |
L |
9.4477445216219 |
L(r)(E,1)/r! |
Ω |
0.17052600680847 |
Real period |
R |
13.850885123164 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999982618 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368fc1 2574m1 27456bi1 |
Quadratic twists by: -4 8 -3 |