Atkin-Lehner |
11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
64009d |
Isogeny class |
Conductor |
64009 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
303600 |
Modular degree for the optimal curve |
Δ |
-2884800683080019 = -1 · 117 · 236 |
Discriminant |
Eigenvalues |
2 -1 -1 -2 11- -4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-21336,2856105] |
[a1,a2,a3,a4,a6] |
Generators |
[-694:16089:8] |
Generators of the group modulo torsion |
j |
-4096/11 |
j-invariant |
L |
6.2665122066808 |
L(r)(E,1)/r! |
Ω |
0.39897252647816 |
Real period |
R |
3.9266564674901 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001429 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5819a1 121d1 |
Quadratic twists by: -11 -23 |