Atkin-Lehner |
3- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
33033t |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
51744 |
Modular degree for the optimal curve |
Δ |
-7080916916073 = -1 · 3 · 7 · 1110 · 13 |
Discriminant |
Eigenvalues |
1 3- 0 7+ 11- 13+ -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-7626,-287135] |
[a1,a2,a3,a4,a6] |
Generators |
[749475476493208685:-3637267307415255770:6762098247997301] |
Generators of the group modulo torsion |
j |
-1890625/273 |
j-invariant |
L |
7.4484067624747 |
L(r)(E,1)/r! |
Ω |
0.25342108422465 |
Real period |
R |
29.391424889777 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099t1 33033bb1 |
Quadratic twists by: -3 -11 |