Atkin-Lehner |
2- 3- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984bj |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-704692224 = -1 · 214 · 36 · 59 |
Discriminant |
Eigenvalues |
2- 3- -1 -1 -4 -2 -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9948,-381904] |
[a1,a2,a3,a4,a6] |
Generators |
[95832:556172:729] |
Generators of the group modulo torsion |
j |
-9115564624/59 |
j-invariant |
L |
4.2752521506332 |
L(r)(E,1)/r! |
Ω |
0.23902066271967 |
Real period |
R |
8.943268966766 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33984u1 8496h1 3776v1 |
Quadratic twists by: -4 8 -3 |