Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400bm |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-443232000000 = -1 · 211 · 36 · 56 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 3 2 -1 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1875,-44750] |
[a1,a2,a3,a4,a6] |
j |
-31250/19 |
j-invariant |
L |
2.8237977531782 |
L(r)(E,1)/r! |
Ω |
0.35297472060788 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200bf1 7600a1 2736e1 |
Quadratic twists by: -4 -3 5 |