Abstract
By representing a genus one curve as a plane curve with five double points, we are able to construct a 3- parameter family of genus one curves over Q with Jacobians having a torsion subgroup isomorphic to Z5. This leads, by specializing the parameters, to elliptic curves over Q of the Mordell-Weil group with high rank and with a torsion subgroup isomorphic to Z5. We also show this family contains as a subfamily the principal homogeneous space parameterizing elliptic curves with a rational point of order 5, namely X1(5). We explicitly describe these families by equations in the Weierstrass form.
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