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Hot answers tagged hyperelliptic-curves

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rational points of a hyperelliptic curve

By now there is a fairly rich literature on computing the set of rational points on curves of higher genus, see for example my survey paper on "Rational points on curves". What one can do for your ...
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Rational perfect power values of $y(y+1)$

There are no such solutions. Let $x=a/b$ and $y=c/d$ be reduced fractions. Then $a^n/b^n=(c(c+d))/d^2$ and since both sides are reduced fractions we get that $a^n=c(c+d)$ and $b^n=d^2$. From the ...
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rational points of a hyperelliptic curve of genus 3

It turns out that $C(K) = C(\mathbb Q) = \{\infty_+, \infty_-, (0,1), (0,-1), (1,1), (1,-1)\}$. To see this, consider a point $P \in C(K)$ and write $\bar{P}$ for its image under the nontrivial ...
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