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https://doi.org/10.3336/gm.47.1.06

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

Petra Tadic ; Martićeva 23, 10000 Zagreb, Croatia


Puni tekst: engleski pdf 145 Kb

str. 81-93

preuzimanja: 312

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Sažetak

Let E be the elliptic curve over Q(T) given by the equation
E:Y2=X3-T2X+1.
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.

Ključne riječi

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

Hrčak ID:

82572

URI

https://hrcak.srce.hr/82572

Posjeta: 704 *