Atkin-Lehner |
3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347ba |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4896 |
Modular degree for the optimal curve |
Δ |
-61347 = -1 · 3 · 112 · 132 |
Discriminant |
Eigenvalues |
-1 3- 2 3 11- 13+ 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,3,12] |
[a1,a2,a3,a4,a6] |
Generators |
[11:32:1] |
Generators of the group modulo torsion |
j |
143/3 |
j-invariant |
L |
6.6629290060375 |
L(r)(E,1)/r! |
Ω |
2.620641639121 |
Real period |
R |
2.5424800195411 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000293 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347x1 61347y1 |
Quadratic twists by: -11 13 |