Atkin-Lehner |
2- 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
128064cd |
Isogeny class |
Conductor |
128064 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1935360 |
Modular degree for the optimal curve |
Δ |
-6848663952738484224 = -1 · 224 · 37 · 235 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -1 4 1 -1 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,111039,-125139231] |
[a1,a2,a3,a4,a6] |
Generators |
[1693552330503786719:13017121064887390024:3812280783870313] |
Generators of the group modulo torsion |
j |
577572497126639/26125579653696 |
j-invariant |
L |
6.7919044390008 |
L(r)(E,1)/r! |
Ω |
0.11341908492062 |
Real period |
R |
29.941629505097 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128064bn1 32016y1 |
Quadratic twists by: -4 8 |