Atkin-Lehner |
2- 3+ 5+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
27840cr |
Isogeny class |
Conductor |
27840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
3503082700800000 = 232 · 32 · 55 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 4 -4 4 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-112641,-14232159] |
[a1,a2,a3,a4,a6] |
Generators |
[-156464395:-93970432:912673] |
Generators of the group modulo torsion |
j |
602944222256641/13363200000 |
j-invariant |
L |
5.0620098239502 |
L(r)(E,1)/r! |
Ω |
0.26095216781636 |
Real period |
R |
9.6991143363722 |
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 |
27840bv1 6960bk1 83520fz1 |
Quadratic twists by: -4 8 -3 |