Atkin-Lehner |
2+ 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
33984z |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-12988887072768 = -1 · 225 · 38 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -4 -1 -3 1 7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2892,-183440] |
[a1,a2,a3,a4,a6] |
Generators |
[78:256:1] |
Generators of the group modulo torsion |
j |
-13997521/67968 |
j-invariant |
L |
3.514351036757 |
L(r)(E,1)/r! |
Ω |
0.29429560149781 |
Real period |
R |
1.4926960422064 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33984bp1 1062b1 11328e1 |
Quadratic twists by: -4 8 -3 |