Atkin-Lehner |
2+ 3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
127680c |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-4085760000 = -1 · 214 · 3 · 54 · 7 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 4 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,399,-399] |
[a1,a2,a3,a4,a6] |
Generators |
[65:544:1] |
Generators of the group modulo torsion |
j |
427694384/249375 |
j-invariant |
L |
4.8146436219944 |
L(r)(E,1)/r! |
Ω |
0.81994583154478 |
Real period |
R |
2.9359523081868 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998101009 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680fp1 15960j1 |
Quadratic twists by: -4 8 |