Atkin-Lehner |
2- 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12696l |
Isogeny class |
Conductor |
12696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
52992 |
Modular degree for the optimal curve |
Δ |
778097949752016 = 24 · 33 · 239 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 0 2 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-105447,-13075920] |
[a1,a2,a3,a4,a6] |
Generators |
[69871601605:-912405256495:151419437] |
Generators of the group modulo torsion |
j |
4499456/27 |
j-invariant |
L |
4.9521015881665 |
L(r)(E,1)/r! |
Ω |
0.26503157449793 |
Real period |
R |
18.684949510441 |
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 |
25392l1 101568bk1 38088k1 12696n1 |
Quadratic twists by: -4 8 -3 -23 |