Atkin-Lehner |
3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
53361m |
Isogeny class |
Conductor |
53361 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
61901446886433 = 33 · 76 · 117 |
Discriminant |
Eigenvalues |
1 3+ 4 7- 11- -2 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-10005,-68832] |
[a1,a2,a3,a4,a6] |
Generators |
[-1253140:19703914:42875] |
Generators of the group modulo torsion |
j |
19683/11 |
j-invariant |
L |
9.6353983718843 |
L(r)(E,1)/r! |
Ω |
0.51264628413212 |
Real period |
R |
9.3977062451869 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999623 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
53361n1 1089c1 4851d1 |
Quadratic twists by: -3 -7 -11 |