Atkin-Lehner |
2+ 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
27968c |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
916455424 = 221 · 19 · 23 |
Discriminant |
Eigenvalues |
2+ 1 1 -2 -5 -6 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2465,46271] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:136:1] [35:-64:1] |
Generators of the group modulo torsion |
j |
6321363049/3496 |
j-invariant |
L |
8.9294335685871 |
L(r)(E,1)/r! |
Ω |
1.5536430149988 |
Real period |
R |
1.4368541361149 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27968bu1 874c1 |
Quadratic twists by: -4 8 |