Atkin-Lehner |
5+ 17- 101+ |
Signs for the Atkin-Lehner involutions |
Class |
8585b |
Isogeny class |
Conductor |
8585 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
310133125 = 54 · 173 · 101 |
Discriminant |
Eigenvalues |
-2 -3 5+ -3 -5 -1 17- -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-313,-1956] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:8:1] [-11:12:1] |
Generators of the group modulo torsion |
j |
3391225933824/310133125 |
j-invariant |
L |
1.6800767395366 |
L(r)(E,1)/r! |
Ω |
1.1416890613995 |
Real period |
R |
0.24526186629117 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999893 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77265g1 42925c1 |
Quadratic twists by: -3 5 |