Atkin-Lehner |
2- 3+ 5+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
81840bo |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-56178628110000 = -1 · 24 · 312 · 54 · 11 · 312 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 11+ -4 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5241,390816] |
[a1,a2,a3,a4,a6] |
j |
-995242860396544/3511164256875 |
j-invariant |
L |
1.0992187187871 |
L(r)(E,1)/r! |
Ω |
0.54960935208796 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20460j1 |
Quadratic twists by: -4 |