Atkin-Lehner |
3- 11- 101- |
Signs for the Atkin-Lehner involutions |
Class |
3333f |
Isogeny class |
Conductor |
3333 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
3960 |
Modular degree for the optimal curve |
Δ |
3299340033 = 35 · 113 · 1012 |
Discriminant |
Eigenvalues |
1 3- 2 4 11- -2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-6705,-211841] |
[a1,a2,a3,a4,a6] |
j |
33329357828245513/3299340033 |
j-invariant |
L |
3.9570493045422 |
L(r)(E,1)/r! |
Ω |
0.52760657393896 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
53328j1 9999g1 83325i1 36663i1 |
Quadratic twists by: -4 -3 5 -11 |