Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400bf |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
-1282554121500000000 = -1 · 28 · 39 · 59 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 0 -4 2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,144825,-50188250] |
[a1,a2,a3,a4,a6] |
j |
115203799856/439833375 |
j-invariant |
L |
1.1047814078209 |
L(r)(E,1)/r! |
Ω |
0.13809767567612 |
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 |
34200ba1 22800u1 13680t1 |
Quadratic twists by: -4 -3 5 |