Atkin-Lehner |
2+ 3- 43- |
Signs for the Atkin-Lehner involutions |
Class |
4128d |
Isogeny class |
Conductor |
4128 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
480 |
Modular degree for the optimal curve |
Δ |
-3195072 = -1 · 26 · 33 · 432 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 2 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,22,84] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:6:1] |
Generators of the group modulo torsion |
j |
17576000/49923 |
j-invariant |
L |
4.3148589800733 |
L(r)(E,1)/r! |
Ω |
1.7719123921186 |
Real period |
R |
0.81171413050021 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4128a1 8256ba2 12384n1 103200bl1 |
Quadratic twists by: -4 8 -3 5 |