Atkin-Lehner |
2+ 3- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984q |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
25088 |
Modular degree for the optimal curve |
Δ |
-2818768896 = -1 · 216 · 36 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -3 3 6 6 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-684,7344] |
[a1,a2,a3,a4,a6] |
j |
-740772/59 |
j-invariant |
L |
2.8084964563225 |
L(r)(E,1)/r! |
Ω |
1.4042482281572 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33984cb1 4248d1 3776k1 |
Quadratic twists by: -4 8 -3 |