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<p>We show that Mochizuki’s initial theta data is computable from an elliptic curve defined over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1100_Article_IEq1.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>. We work out the case of initial theta data for the elliptic curve with Cremona label <Emphasis FontCategory="SansSerif">11a1</Emphasis> in detail.</p>

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The statement of Mochizuki’s corollary 3.12: initial theta data

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Taylor Dupuy,
  • Anton Hilado

摘要

We show that Mochizuki’s initial theta data is computable from an elliptic curve defined over \(\mathbb {Q}\) Q . We work out the case of initial theta data for the elliptic curve with Cremona label 11a1 in detail.