Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168f |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
6587088320592 = 24 · 38 · 137 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 0 13+ -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59826,-5630911] |
[a1,a2,a3,a4,a6] |
Generators |
[-140:27:1] [325:3042:1] |
Generators of the group modulo torsion |
j |
420616192/117 |
j-invariant |
L |
5.4490450791894 |
L(r)(E,1)/r! |
Ω |
0.30527013066763 |
Real period |
R |
2.2312390452653 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999975 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24336l1 97344bx1 4056m1 936i1 |
Quadratic twists by: -4 8 -3 13 |