Atkin-Lehner |
3- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
32307j |
Isogeny class |
Conductor |
32307 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18240 |
Modular degree for the optimal curve |
Δ |
-5203074657 = -1 · 3 · 117 · 89 |
Discriminant |
Eigenvalues |
1 3- 2 4 11- -3 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-245,3749] |
[a1,a2,a3,a4,a6] |
j |
-912673/2937 |
j-invariant |
L |
4.7792647842123 |
L(r)(E,1)/r! |
Ω |
1.1948161960538 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96921t1 2937b1 |
Quadratic twists by: -3 -11 |