Atkin-Lehner |
3+ 7+ 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
27489b |
Isogeny class |
Conductor |
27489 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
151200 |
Modular degree for the optimal curve |
Δ |
2971225078404891 = 3 · 78 · 112 · 175 |
Discriminant |
Eigenvalues |
-1 3+ -1 7+ 11+ -5 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-93346,-10698220] |
[a1,a2,a3,a4,a6] |
Generators |
[412:-4788:1] [-1434:5201:8] |
Generators of the group modulo torsion |
j |
15603672287329/515408091 |
j-invariant |
L |
4.3015561318738 |
L(r)(E,1)/r! |
Ω |
0.27368746224182 |
Real period |
R |
0.52390125298872 |
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 |
82467j1 27489q1 |
Quadratic twists by: -3 -7 |