Atkin-Lehner |
2+ 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8272b |
Isogeny class |
Conductor |
8272 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
21120 |
Modular degree for the optimal curve |
Δ |
-91074984704 = -1 · 28 · 115 · 472 |
Discriminant |
Eigenvalues |
2+ 3 -1 4 11+ -4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6868,-219556] |
[a1,a2,a3,a4,a6] |
j |
-139950548941824/355761659 |
j-invariant |
L |
4.7191997359444 |
L(r)(E,1)/r! |
Ω |
0.26217776310802 |
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 |
4136b1 33088bn1 74448l1 90992h1 |
Quadratic twists by: -4 8 -3 -11 |