Elliptic curves of rank one over number fields

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arxiv 2505.16910 v1 pith:NME2Z5Z6 submitted 2025-05-22 math.NT

Peter Koymans , Carlo Pagano This is my paper

classification math.NT

keywords curvesellipticnumberrankequaleveryexactlyexist

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abstract

We prove that for every number field $K$, there exist infinitely many elliptic curves $E$ over $K$ with rank exactly equal to 1.

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Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
math.NT 2025-05 unverdicted novelty 6.0 of 10

For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.