Atkin-Lehner |
2+ 3+ 5+ 17+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
59160a |
Isogeny class |
Conductor |
59160 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12672 |
Modular degree for the optimal curve |
Δ |
-32183040 = -1 · 28 · 3 · 5 · 172 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 1 -4 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,79,-75] |
[a1,a2,a3,a4,a6] |
Generators |
[1:2:1] [4:17:1] |
Generators of the group modulo torsion |
j |
210308096/125715 |
j-invariant |
L |
8.1013264663664 |
L(r)(E,1)/r! |
Ω |
1.2128485381339 |
Real period |
R |
0.83494828616715 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
118320m1 |
Quadratic twists by: -4 |