Atkin-Lehner |
3+ 5- 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
17085b |
Isogeny class |
Conductor |
17085 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
104832 |
Modular degree for the optimal curve |
Δ |
-4227413645607615 = -1 · 33 · 5 · 178 · 672 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 4 6 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-15215,-3216868] |
[a1,a2,a3,a4,a6] |
j |
-389530408392866161/4227413645607615 |
j-invariant |
L |
1.6755390663837 |
L(r)(E,1)/r! |
Ω |
0.18617100737596 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51255c1 85425k1 |
Quadratic twists by: -3 5 |