Atkin-Lehner |
2- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
59488r |
Isogeny class |
Conductor |
59488 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
159744 |
Modular degree for the optimal curve |
Δ |
-404289197019136 = -1 · 212 · 112 · 138 |
Discriminant |
Eigenvalues |
2- 0 1 -2 11- 13+ -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,8788,913952] |
[a1,a2,a3,a4,a6] |
Generators |
[-68:44:1] |
Generators of the group modulo torsion |
j |
22464/121 |
j-invariant |
L |
4.79607843827 |
L(r)(E,1)/r! |
Ω |
0.38395177357251 |
Real period |
R |
3.1228390960372 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000521 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
59488a1 118976b1 59488b1 |
Quadratic twists by: -4 8 13 |