Atkin-Lehner |
3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
33033k |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
26 |
Product of Tamagawa factors cp |
deg |
2951520 |
Modular degree for the optimal curve |
Δ |
-2.4299753226889E+21 |
Discriminant |
Eigenvalues |
0 3+ 2 7- 11- 13+ 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-72034607,235356539186] |
[a1,a2,a3,a4,a6] |
Generators |
[4754:18007:1] |
Generators of the group modulo torsion |
j |
-192843857539240787968/11336014217619 |
j-invariant |
L |
4.3082768432056 |
L(r)(E,1)/r! |
Ω |
0.1373196720201 |
Real period |
R |
1.2066949554297 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099bp1 33033c1 |
Quadratic twists by: -3 -11 |