Atkin-Lehner |
3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033r |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
16267680 |
Modular degree for the optimal curve |
Δ |
-2.544759257015E+26 |
Discriminant |
Eigenvalues |
-2 3- -2 7+ 11+ 13- 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-41324444,774272658308] |
[a1,a2,a3,a4,a6] |
Generators |
[40938:8227576:1] |
Generators of the group modulo torsion |
j |
-3309867537183567872/107922634023138753 |
j-invariant |
L |
2.353916660484 |
L(r)(E,1)/r! |
Ω |
0.046170408810388 |
Real period |
R |
5.0983231925684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099n1 33033y1 |
Quadratic twists by: -3 -11 |