Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168d |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
18720 |
Modular degree for the optimal curve |
Δ |
9514683129744 = 24 · 36 · 138 |
Discriminant |
Eigenvalues |
2+ 3- -2 -1 -1 13+ -3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6591,-142805] |
[a1,a2,a3,a4,a6] |
j |
3328 |
j-invariant |
L |
1.0843555139439 |
L(r)(E,1)/r! |
Ω |
0.54217775697195 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24336j1 97344bt1 1352c1 12168o1 |
Quadratic twists by: -4 8 -3 13 |