Skip to the main content

Original scientific paper

On the family of elliptic curves Y^2=X^3-T^2X+1

Petra Tadic ; Martićeva 23, 10000 Zagreb, Croatia

Full text: english pdf 145 Kb

page 81-93

downloads: 319



Let E be the elliptic curve over Q(T) given by the equation
We prove that the torsion subgroup of the group E(C(T)) is trivial, rankQ(T)(E)=3 and rankC(T)(E)=4. We find a parametrization of E of rank at least four over the function field Q(a,i,s,n,k) where s2=i3-a2i. From this we get a family of rank ≥ 5 over the field of rational functions in two variables and a family of rank ≥ 6 over an elliptic curve of positive rank. We also found particular elliptic curves with rank ≥ 11.


Elliptic surface, elliptic curve, parametrization, function field, rank, family of elliptic curves, torsion

Hrčak ID:



Visits: 724 *