Atkin-Lehner |
2+ 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
12936h |
Isogeny class |
Conductor |
12936 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
39744 |
Modular degree for the optimal curve |
Δ |
-1463891159808 = -1 · 28 · 39 · 74 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 11+ -5 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5945,183819] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:-462:1] [-75:462:1] |
Generators of the group modulo torsion |
j |
-37811178496/2381643 |
j-invariant |
L |
6.2037319437835 |
L(r)(E,1)/r! |
Ω |
0.83783352821686 |
Real period |
R |
0.034280057140164 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25872b1 103488k1 38808ca1 12936e1 |
Quadratic twists by: -4 8 -3 -7 |