Atkin-Lehner |
2- 3- 67- |
Signs for the Atkin-Lehner involutions |
Class |
9648s |
Isogeny class |
Conductor |
9648 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
-12503808 = -1 · 28 · 36 · 67 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 -4 -6 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,24,-164] |
[a1,a2,a3,a4,a6] |
Generators |
[5:9:1] [6:14:1] |
Generators of the group modulo torsion |
j |
8192/67 |
j-invariant |
L |
5.1440898517962 |
L(r)(E,1)/r! |
Ω |
1.1159686277753 |
Real period |
R |
1.1523822721725 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2412b1 38592bx1 1072b1 |
Quadratic twists by: -4 8 -3 |