Atkin-Lehner |
3+ 5+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
8835b |
Isogeny class |
Conductor |
8835 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
80640 |
Modular degree for the optimal curve |
Δ |
-95367146430234375 = -1 · 33 · 57 · 196 · 312 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 4 -2 6 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-26931,14943744] |
[a1,a2,a3,a4,a6] |
j |
-2160141297033678769/95367146430234375 |
j-invariant |
L |
1.1219352526068 |
L(r)(E,1)/r! |
Ω |
0.2804838131517 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
26505j1 44175h1 |
Quadratic twists by: -3 5 |