Atkin-Lehner |
2- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
682a |
Isogeny class |
Conductor |
682 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
Δ |
-146192756842 = -1 · 2 · 119 · 31 |
Discriminant |
Eigenvalues |
2- -2 0 -1 11+ -4 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-2003,-39269] |
[a1,a2,a3,a4,a6] |
Generators |
[1054:10753:8] |
Generators of the group modulo torsion |
j |
-888751018248625/146192756842 |
j-invariant |
L |
2.2812508095831 |
L(r)(E,1)/r! |
Ω |
0.35363003593532 |
Real period |
R |
6.4509531933548 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5456h3 21824m3 6138i3 17050b3 |
Quadratic twists by: -4 8 -3 5 |