Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168t |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
7303822813667294928 = 24 · 316 · 139 |
Discriminant |
Eigenvalues |
2- 3- 4 0 -2 13+ -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-990678,-356562115] |
[a1,a2,a3,a4,a6] |
Generators |
[17840650:14484501:15625] |
Generators of the group modulo torsion |
j |
1909913257984/129730653 |
j-invariant |
L |
5.8901805159774 |
L(r)(E,1)/r! |
Ω |
0.15197348486951 |
Real period |
R |
9.6894871513854 |
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 |
24336q1 97344cx1 4056d1 936d1 |
Quadratic twists by: -4 8 -3 13 |