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Sc."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>Determining the rank of an elliptic curve [Formula: see text] remains a central challenge in number theory. Heuristics such as Mestre\u2013Nagao sums are widely used to estimate ranks, but there is considerable room for improving their predictive power. This paper introduces two novel methods for enhancing rank classification using Mestre\u2013Nagao sums. First, we propose a \u201cmulti-value\u201d approach that simultaneously uses two distinct sums, [Formula: see text] and [Formula: see text], evaluated over multiple ranges. This multi-sum perspective significantly improves classification accuracy over traditional single-sum heuristics. Second, we employ machine learning \u2014 specifically deep neural networks \u2014 to learn optimal, potentially conductor-dependent weightings for Mestre\u2013Nagao sums directly from data. Our results indicate that adaptively weighted sums offer a slight edge in rank classification over traditional methods.<\/jats:p>","DOI":"10.1142\/s2810939225400040","type":"journal-article","created":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T03:34:23Z","timestamp":1760672063000},"page":"75-86","source":"Crossref","is-referenced-by-count":0,"title":["Improving elliptic curve rank classification using multi-value and learned Mestre\u2013Nagao sums"],"prefix":"10.1142","volume":"03","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1193-9876","authenticated-orcid":false,"given":"Zvonimir","family":"Bujanovi\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Zagreb, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0147-7914","authenticated-orcid":false,"given":"Matija","family":"Kazalicki","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Zagreb, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6044-7061","authenticated-orcid":false,"given":"Domagoj","family":"Vlah","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,10,25]]},"reference":[{"key":"S2810939225400040BIB001","doi-asserted-by":"crossref","unstructured":"A. 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