Atkin-Lehner |
2- 7+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
32186r |
Isogeny class |
Conductor |
32186 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
722304 |
Modular degree for the optimal curve |
Δ |
-4406383424579122756 = -1 · 22 · 76 · 1110 · 192 |
Discriminant |
Eigenvalues |
2- -2 -3 7+ 11- 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-395612,-139219244] |
[a1,a2,a3,a4,a6] |
Generators |
[20616:2948410:1] |
Generators of the group modulo torsion |
j |
-264000833833/169885156 |
j-invariant |
L |
3.8590244098846 |
L(r)(E,1)/r! |
Ω |
0.092500548915257 |
Real period |
R |
5.2148669050331 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32186n1 |
Quadratic twists by: -11 |