Atkin-Lehner |
2+ 3+ 17- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
59568d |
Isogeny class |
Conductor |
59568 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8448 |
Modular degree for the optimal curve |
Δ |
-8577792 = -1 · 28 · 33 · 17 · 73 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -1 -2 -4 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,12,-144] |
[a1,a2,a3,a4,a6] |
Generators |
[5:4:1] [8:20:1] |
Generators of the group modulo torsion |
j |
686000/33507 |
j-invariant |
L |
8.1491036240197 |
L(r)(E,1)/r! |
Ω |
1.1118738960258 |
Real period |
R |
3.6645808725004 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
29784e1 |
Quadratic twists by: -4 |