Gonality of the modular curve $X_0(N)$
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- by Filip Najman and Petar Orlić;
- Math. Comp. 93 (2024), 863-886
- DOI: https://doi.org/10.1090/mcom/3873
- Published electronically: July 13, 2023
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Abstract:
In this paper we determine the $\mathbb {Q}$-gonalities of the modular curves $X_0(N)$ for all $N<145$. We determine the $\mathbb {C}$-gonality of many of these curves and the $\mathbb {Q}$-gonalities and $\mathbb {C}$-gonalities for many larger values of $N$.
Using these results and some further work, we determine all the modular curves $X_0(N)$ of gonality $4$, $5$ and $6$ over $\mathbb {Q}$. We also find the first known instances of pentagonal curves $X_0(N)$ over $\mathbb {C}$.
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Bibliographic Information
- Filip Najman
- Affiliation: University of Zagreb, Bijenička Cesta 30, 10000 Zagreb, Croatia
- MR Author ID: 886852
- ORCID: 0000-0002-0994-0846
- Email: fnajman@math.hr
- Petar Orlić
- Affiliation: University of Zagreb, Bijenička Cesta 30, 10000 Zagreb, Croatia
- ORCID: 0009-0009-9183-8071
- Email: petar.orlic@math.hr
- Received by editor(s): December 6, 2022
- Received by editor(s) in revised form: April 8, 2023, and May 7, 2023
- Published electronically: July 13, 2023
- Additional Notes: The authors were supported by the 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) and by the Croatian Science Foundation under the project no. IP-2018-01-1313.
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp. 93 (2024), 863-886
- MSC (2020): Primary 11G18, 14H51
- DOI: https://doi.org/10.1090/mcom/3873
- MathSciNet review: 4678587