Atkin-Lehner |
2- 7+ 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
89012f |
Isogeny class |
Conductor |
89012 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-55461953008 = -1 · 24 · 73 · 112 · 174 |
Discriminant |
Eigenvalues |
2- 0 0 7+ 11+ 4 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1445,-23987] |
[a1,a2,a3,a4,a6] |
Generators |
[51:187:1] |
Generators of the group modulo torsion |
j |
-249696000/41503 |
j-invariant |
L |
5.1687971668052 |
L(r)(E,1)/r! |
Ω |
0.38367747195851 |
Real period |
R |
0.74842913367938 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007161 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89012v1 |
Quadratic twists by: 17 |