Atkin-Lehner |
23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
32269a |
Isogeny class |
Conductor |
32269 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
21780 |
Modular degree for the optimal curve |
Δ |
-9030189229 = -1 · 236 · 61 |
Discriminant |
Eigenvalues |
-1 -2 3 -1 5 1 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1069,-14298] |
[a1,a2,a3,a4,a6] |
Generators |
[4945:6977:125] |
Generators of the group modulo torsion |
j |
-912673/61 |
j-invariant |
L |
3.0325589218827 |
L(r)(E,1)/r! |
Ω |
0.41586343203969 |
Real period |
R |
7.2921990447899 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61a1 |
Quadratic twists by: -23 |