Atkin-Lehner |
2+ 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
13728b |
Isogeny class |
Conductor |
13728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12672 |
Modular degree for the optimal curve |
Δ |
-4421816256 = -1 · 26 · 3 · 116 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 11+ 13+ 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-874,10744] |
[a1,a2,a3,a4,a6] |
Generators |
[15:28:1] |
Generators of the group modulo torsion |
j |
-1154981015488/69090879 |
j-invariant |
L |
3.97593473538 |
L(r)(E,1)/r! |
Ω |
1.3600722794173 |
Real period |
R |
2.9233260581442 |
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 |
13728m1 27456bh1 41184be1 |
Quadratic twists by: -4 8 -3 |