Atkin-Lehner |
2+ 3+ 5+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
27840r |
Isogeny class |
Conductor |
27840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
2770993152000 = 220 · 36 · 53 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -4 0 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3681,32481] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:256:1] [-45:324:1] |
Generators of the group modulo torsion |
j |
21047437081/10570500 |
j-invariant |
L |
6.2267750942762 |
L(r)(E,1)/r! |
Ω |
0.7138197800863 |
Real period |
R |
4.3615876639915 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27840dt1 870c1 83520cl1 |
Quadratic twists by: -4 8 -3 |