Atkin-Lehner |
2+ 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168d |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
126720 |
Modular degree for the optimal curve |
Δ |
-5194752 = -1 · 210 · 3 · 19 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 0 5 5 7 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10768,-426512] |
[a1,a2,a3,a4,a6] |
j |
-134855675090500/5073 |
j-invariant |
L |
4.2179840815134 |
L(r)(E,1)/r! |
Ω |
0.23433245117166 |
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 |
40584be1 |
Quadratic twists by: -4 |