Atkin-Lehner |
2- 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
8272o |
Isogeny class |
Conductor |
8272 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-91074984704 = -1 · 28 · 115 · 472 |
Discriminant |
Eigenvalues |
2- -1 -1 -4 11- -2 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,619,-13463] |
[a1,a2,a3,a4,a6] |
Generators |
[101:1034:1] |
Generators of the group modulo torsion |
j |
102294880256/355761659 |
j-invariant |
L |
2.4427092173326 |
L(r)(E,1)/r! |
Ω |
0.54623006742832 |
Real period |
R |
0.2235971033994 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2068b1 33088w1 74448ba1 90992p1 |
Quadratic twists by: -4 8 -3 -11 |