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- W3120485641 abstract "Abstract This note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over $$mathbb {Q}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Q</mml:mi></mml:math> in a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point. The main result is that explicit examples are provided of ‘pointless’ genus one curves over $$mathbb {Q}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Q</mml:mi></mml:math> corresponding to the torsion orders 7, 8, 9, 10, 12 (and hence, all possibilities) occurring in Mazur’s theorem. In fact three distinct methods are proposed for constructing such examples, each involving different in our opinion quite nice ideas from the arithmetic of elliptic curves or from algebraic geometry." @default.
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- W3120485641 date "2021-01-06" @default.
- W3120485641 modified "2023-10-16" @default.
- W3120485641 title "Mazur’s rational torsion result for pointless genus one curves: examples" @default.
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- W3120485641 doi "https://doi.org/10.1007/s40993-020-00231-z" @default.
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