Atkin-Lehner |
2+ 3+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984a |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
106904420352 = 226 · 33 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -4 4 2 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1260,-6992] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:80:1] |
Generators of the group modulo torsion |
j |
31255875/15104 |
j-invariant |
L |
4.8787844883743 |
L(r)(E,1)/r! |
Ω |
0.84099233545272 |
Real period |
R |
2.9006117432381 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33984bd1 1062g1 33984d1 |
Quadratic twists by: -4 8 -3 |