Atkin-Lehner |
2+ 3- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984n |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-22550151168 = -1 · 219 · 36 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -2 -3 -1 3 -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2316,43504] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:288:1] [30:32:1] |
Generators of the group modulo torsion |
j |
-7189057/118 |
j-invariant |
L |
7.2552955025793 |
L(r)(E,1)/r! |
Ω |
1.2068865486952 |
Real period |
R |
0.75144754807547 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33984by1 1062e1 3776i1 |
Quadratic twists by: -4 8 -3 |