Large torsion subgroups of split Jacobians of curves of genus two or three

Details Large torsion subgroups of split Jacobians of curves of genus two or three Large torsion subgroups of split Jacobians of curves of genus two or three

1998-09-08

arxiv.org/abs/math/9809210v1

Forum Math. 12, no. 3 (2000), 315--364

Mathematics

Number Theory

Scientific paper

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^1 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^4 + Y^4 + Z^4) - 96914(X^2 Y^2 + X^2 Z^2 + Y^2 Z^2) = 0, whose Jacobian has 864 rational torsion points. This paper has appeared in Forum Math. 12 (2000) 315-364.

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