Atkin-Lehner |
2+ 7- 29- 31- |
Signs for the Atkin-Lehner involutions |
Class |
12586c |
Isogeny class |
Conductor |
12586 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2816 |
Modular degree for the optimal curve |
Δ |
8633996 = 22 · 74 · 29 · 31 |
Discriminant |
Eigenvalues |
2+ 0 -1 7- -2 -4 -7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-140,-588] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:7:1] [-6:6:1] |
Generators of the group modulo torsion |
j |
304685358489/8633996 |
j-invariant |
L |
4.5882558800629 |
L(r)(E,1)/r! |
Ω |
1.3898702314143 |
Real period |
R |
0.41265146345659 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
100688r1 113274br1 88102d1 |
Quadratic twists by: -4 -3 -7 |