Atkin-Lehner |
2+ 19- 23- |
Signs for the Atkin-Lehner involutions |
Class |
27968o |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-164675584 = -1 · 214 · 19 · 232 |
Discriminant |
Eigenvalues |
2+ 0 -1 -5 -3 -4 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,112,416] |
[a1,a2,a3,a4,a6] |
Generators |
[1:23:1] |
Generators of the group modulo torsion |
j |
9483264/10051 |
j-invariant |
L |
2.4541270265451 |
L(r)(E,1)/r! |
Ω |
1.2018106950418 |
Real period |
R |
1.0210123094552 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27968ba1 3496g1 |
Quadratic twists by: -4 8 |