Atkin-Lehner |
3- 11+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
17589b |
Isogeny class |
Conductor |
17589 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-55563651 = -1 · 36 · 11 · 132 · 41 |
Discriminant |
Eigenvalues |
-1 3- -3 -5 11+ 13+ 3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-22,359] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:17:1] [-1:20:1] |
Generators of the group modulo torsion |
j |
-1180932193/55563651 |
j-invariant |
L |
4.1794933034608 |
L(r)(E,1)/r! |
Ω |
1.6484127089833 |
Real period |
R |
0.21128877903191 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52767h1 |
Quadratic twists by: -3 |