Atkin-Lehner |
2- 23+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
8188b |
Isogeny class |
Conductor |
8188 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
852 |
Modular degree for the optimal curve |
Δ |
-32752 = -1 · 24 · 23 · 89 |
Discriminant |
Eigenvalues |
2- 0 2 -3 0 0 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-209,-1163] |
[a1,a2,a3,a4,a6] |
Generators |
[2532:24209:27] |
Generators of the group modulo torsion |
j |
-63101922048/2047 |
j-invariant |
L |
4.2838480253828 |
L(r)(E,1)/r! |
Ω |
0.62781565685578 |
Real period |
R |
6.8234169992464 |
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 |
32752k1 73692b1 |
Quadratic twists by: -4 -3 |