Atkin-Lehner |
2+ 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
33984w |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
4870832652288 = 222 · 39 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 4 6 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-19884,1073968] |
[a1,a2,a3,a4,a6] |
Generators |
[-156:616:1] |
Generators of the group modulo torsion |
j |
4549540393/25488 |
j-invariant |
L |
7.4056819785116 |
L(r)(E,1)/r! |
Ω |
0.77374872512189 |
Real period |
R |
4.785585900219 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33984bl1 1062h1 11328d1 |
Quadratic twists by: -4 8 -3 |