Some interesting curves of genus 2 to 7 (Q1377600)
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scientific article; zbMATH DE number 1109652
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some interesting curves of genus 2 to 7 |
scientific article; zbMATH DE number 1109652 |
Statements
Some interesting curves of genus 2 to 7 (English)
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16 February 1998
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The author presents 4 examples of algebraic curves \(C\) defined over \(\mathbb Q\) of genus 2, 4, 6, 7 respectively having the following properties: (i) The Jacobian of \(C\) is \(\mathbb Q\)-isogenous to a product of elliptic curves. (ii) Each factor of the Jacobian has positive Mordell-Weil rank over \(\mathbb Q\). (iii) The curve \(C\) possesses a point in \(\mathbb R\) and in all \(p\)-adic fields \(\mathbb Q_p\). (iv) The curve \(C\) has no point over \(\mathbb Q\).
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Hasse principle
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genus 2
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algebraic curves
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Jacobian
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Mordell-Weil rank
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0.8768142
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0.87655956
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0.8630197
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