Atkin-Lehner |
2- 3- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984bh |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
-613258407936 = -1 · 212 · 36 · 593 |
Discriminant |
Eigenvalues |
2- 3- 1 3 0 0 -2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18612,978048] |
[a1,a2,a3,a4,a6] |
Generators |
[28:692:1] |
Generators of the group modulo torsion |
j |
-238789577664/205379 |
j-invariant |
L |
6.9022290966282 |
L(r)(E,1)/r! |
Ω |
0.90854887880357 |
Real period |
R |
3.7984907899054 |
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 |
33984bu1 16992d1 3776z1 |
Quadratic twists by: -4 8 -3 |