Large Torsion Subgroups of Split Jacobians of Curves of Genus Two or Three
نویسندگان
چکیده
We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational points on a certain elliptic surface over P of positive rank parameterize a family of genus-2 curves over Q whose Jacobians each have 128 rational torsion points. Also, we find the genus-3 curve 15625(X + Y 4 + Z)− 96914(XY 2 + XZ + Y Z) = 0, whose Jacobian has 864 rational torsion points.
منابع مشابه
Large Torsion Subgroups of Split Jacobians of Curves of Genus Two or Three Everett W. Howe, Franck Leprévost, and Bjorn Poonen
We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational points on a certain elliptic surface over P of positive rank parameterize a family of genus-2 curves over Q whose Jacobians each have 128 rational torsion points. Also, we find the genus-3 curve 15625(X4 + Y 4 + Z4)− 969...
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