{
  "abstract": "Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields, assuming that their associated L -functions are analytic L -functions. Moreover, we obtain lower bounds for the conductor of elliptic curves and abelian varieties over Q with specified bad reduction, under the same hypothesis. As an application, we prove, for certain number fields, the non-existence of abelian varieties with analytic L -function and with everywhere good reduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Pierre Tchamitchian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6s3ak79gdz4a.bib",
  "cited_by": 0,
  "doi": "10.1016/j.jnt.2026.06.014",
  "fulltext_url": null,
  "id": "d6s3ak79gdz4a",
  "issns": [
    "0022-314X",
    "1096-1658"
  ],
  "landing_url": "https://hal.science/hal-05838589v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7170652871",
  "pdf_url": "https://www.sciencedirect.com/science/article/pii/S0022314X26001460/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/d6s3ak79gdz4a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05838589",
      "source": "hal",
      "url": "https://hal.science/hal-05838589v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields",
  "title_text": "Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/d6s3ak79gdz4a",
  "venue": "Journal of Number Theory",
  "versions": []
}