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<p>We determine all modular curves <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1083_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="93" /> </InlineMediaObject> <EquationSource Format="TEX">\(X_0(N)/\langle w_d\rangle \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <mrow> <mo stretchy="false">⟨</mo> <msub> <mi>w</mi> <mi>d</mi> </msub> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> that admit infinitely many cubic points over the rational field <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1083_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation>, when <i>N</i> is square-free.</p>

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Infinitely many cubic points on \(X_0(N)/\langle w_d\rangle \) with N square-free

  • 期刊论文

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  • 发表日期：

    2025年5月26日

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  • Francesc Bars Cortina,
  • Tarun Dalal

摘要

We determine all modular curves \(X_0(N)/\langle w_d\rangle \) X 0 ( N ) / ⟨ w d ⟩ that admit infinitely many cubic points over the rational field \(\mathbb {Q}\) Q , when N is square-free.