{
  "abstract": "Let M be an imaginary quadratic field and A be an abelian variety of odd dimension g defined over Q for which there is a unitary algebra embedding of M in End^0(A_M) of signature ((g+1)/2,(g-1)/2). Extending a result by Fité and Goodman, we show the existence of an elliptic curve E over Q with complex multiplication by M such that H_et^1(E_Qbar, Q_l) is a G_Q-subrepresentation of H_et^g ( A_Qbar, Q_l((g-1)/2) ). The main results of the article consist on explicit descriptions of E for A in two different families. First, when A is the Jacobian of the curve y^2 = xh(x^2), where h in Z[x] is a degree g monic separable polynomial with nonzero h(0), we show that E is given by y^2 = x^3 + h(0)x. Second, when A is the Jacobian of y^3=f(x), where h in Z[x] is a degree 4 monic separable polynomial, we show that E is given by y^2 = x^3 + 16 disc(f). This latter result builds on work by Laga and Shnidman in the bielliptic case, of which we give an alternative proof by means of a new p-adic method. As an application, we derive a practical average polynomial time algorithm to compute the Zeta functions of the reductions of a Picard curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19069",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesc Fité"
    },
    {
      "name": "Francesc Pedret"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9msavqz7jnfz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19069",
  "fulltext_url": null,
  "id": "9msavqz7jnfz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19069",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222089025",
  "pdf_url": "https://arxiv.org/pdf/2610.19069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9msavqz7jnfz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19069"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Elliptic curves attached to Jacobians with imaginary multiplication",
  "title_text": "Elliptic curves attached to Jacobians with imaginary multiplication",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/9msavqz7jnfz5",
  "venue": "arXiv",
  "versions": []
}