Atkin-Lehner |
2+ 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
83824f |
Isogeny class |
Conductor |
83824 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
198912 |
Modular degree for the optimal curve |
Δ |
-497972230912 = -1 · 28 · 137 · 31 |
Discriminant |
Eigenvalues |
2+ 0 4 -2 3 13+ 8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-15548,-746980] |
[a1,a2,a3,a4,a6] |
j |
-336393216/403 |
j-invariant |
L |
3.8476206711252 |
L(r)(E,1)/r! |
Ω |
0.21375669820412 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41912f1 6448c1 |
Quadratic twists by: -4 13 |