Computing Quadratic Points on Modular Curves X0(N)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Nikola Adžaga
  • Timo Keller
  • Philippe Michaud-Jacobs
  • Filip Najman
  • Ekin Ozman
  • Borna Vukorepa

Organisationseinheiten

Externe Organisationen

  • University of Zagreb
  • University of Warwick
  • Bogazici University
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Details

OriginalspracheEnglisch
Seiten (von - bis)1371-1397
Seitenumfang27
FachzeitschriftMathematics of Computation
Jahrgang93
Ausgabenummer347
Frühes Online-Datum3 Okt. 2023
PublikationsstatusVeröffentlicht - Mai 2024

Abstract

In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves X0(N) of genus up to 8, and genus up to 10 with N prime, for which they were previously unknown. The values of N we consider are contained in the set L = {58, 68, 74, 76, 80, 85, 97, 98, 100, 103, 107, 109, 113, 121, 127}. We obtain that all the non-cuspidal quadratic points on X0(N) for N ∈ L are complex multiplication (CM) points, except for one pair of Galois conjugate points on X0(103) defined over Q(√2885). We also compute the j-invariants of the elliptic curves parametrised by these points, and for the CM points determine their geometric endomorphism rings.

ASJC Scopus Sachgebiete

Zitieren

Computing Quadratic Points on Modular Curves X0(N). / Adžaga, Nikola; Keller, Timo; Michaud-Jacobs, Philippe et al.
in: Mathematics of Computation, Jahrgang 93, Nr. 347, 05.2024, S. 1371-1397.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Adžaga, N, Keller, T, Michaud-Jacobs, P, Najman, F, Ozman, E & Vukorepa, B 2024, 'Computing Quadratic Points on Modular Curves X0(N)', Mathematics of Computation, Jg. 93, Nr. 347, S. 1371-1397. https://doi.org/10.48550/arXiv.2303.12566, https://doi.org/10.1090/mcom/3902
Adžaga, N., Keller, T., Michaud-Jacobs, P., Najman, F., Ozman, E., & Vukorepa, B. (2024). Computing Quadratic Points on Modular Curves X0(N). Mathematics of Computation, 93(347), 1371-1397. https://doi.org/10.48550/arXiv.2303.12566, https://doi.org/10.1090/mcom/3902
Adžaga N, Keller T, Michaud-Jacobs P, Najman F, Ozman E, Vukorepa B. Computing Quadratic Points on Modular Curves X0(N). Mathematics of Computation. 2024 Mai;93(347):1371-1397. Epub 2023 Okt 3. doi: 10.48550/arXiv.2303.12566, 10.1090/mcom/3902
Adžaga, Nikola ; Keller, Timo ; Michaud-Jacobs, Philippe et al. / Computing Quadratic Points on Modular Curves X0(N). in: Mathematics of Computation. 2024 ; Jahrgang 93, Nr. 347. S. 1371-1397.
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AU - Adžaga, Nikola

AU - Keller, Timo

AU - Michaud-Jacobs, Philippe

AU - Najman, Filip

AU - Ozman, Ekin

AU - Vukorepa, Borna

N1 - Funding Information: The second author was supported by the Deutsche Forschungsgemeinschaft (DFG), Projektnummer STO 299/18-1, AOBJ: 667349 while working on this article. The third author was supported by an EPSRC studentship EP/R513374/1 and had previously used the surname Michaud- Rodgers. The fourth and sixth authors were supported by QuantiXLie Centre of Excellence, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004). The fifth author was partially supported by TUBITAK Project No 122F413.

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KW - Jacobians

KW - Modular curves

KW - Mordell–Weil sieve

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KW - symmetric Chabauty

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