Crossref Citations
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Shatsila, Anatoli
2023.
Geometry of elliptic normal curves of degree 6.
Communications in Algebra,
p.
1.
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}6$-coverings of elliptic curvesPublished online by Cambridge University Press: 01 August 2014
In this paper we give a new formula for adding
$2$-coverings and
$3$-coverings of elliptic curves that avoids the need for any field extensions. We show that the
$6$-coverings obtained can be represented by pairs of cubic forms. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve. This work has applications to finding rational points of large height on elliptic curves.