Atkin-Lehner |
2+ 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
33088r |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-542113792 = -1 · 220 · 11 · 47 |
Discriminant |
Eigenvalues |
2+ 2 2 -5 11- 3 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-737,8033] |
[a1,a2,a3,a4,a6] |
Generators |
[16:9:1] |
Generators of the group modulo torsion |
j |
-169112377/2068 |
j-invariant |
L |
7.9444286136781 |
L(r)(E,1)/r! |
Ω |
1.6495416189349 |
Real period |
R |
2.4080715886416 |
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 |
33088bc1 1034a1 |
Quadratic twists by: -4 8 |