Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Elliptic Curves: Diophantine Analysis | Statement: [Serge Lang, notableWork, Elliptic Curves: Diophantine Analysis]

Target entity: Elliptic Curves: Diophantine Analysis
Context triple: [Serge Lang, notableWork, Elliptic Curves: Diophantine Analysis]

• A. Arithmetic of Elliptic Curves
  "Arithmetic of Elliptic Curves" is a foundational monograph in number theory that systematically develops the theory of elliptic curves and their arithmetic properties.
• B. Introduction to Elliptic Curves and Modular Forms
  Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
• C. Lectures on Elliptic Curves
  Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
• D. Hasse bound for elliptic curves
  The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
• E. modularity theorem for elliptic curves over Q
  The modularity theorem for elliptic curves over Q is a landmark result in number theory stating that every elliptic curve defined over the rational numbers corresponds to a modular form, a fact central to the proof of Fermat’s Last Theorem.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Elliptic Curves: Diophantine Analysis
Target entity description: "Elliptic Curves: Diophantine Analysis" is a graduate-level mathematics book by Serge Lang that develops the theory of elliptic curves with a focus on their applications to Diophantine equations and number theory.

• A. Arithmetic of Elliptic Curves
  "Arithmetic of Elliptic Curves" is a foundational monograph in number theory that systematically develops the theory of elliptic curves and their arithmetic properties.
• B. Introduction to Elliptic Curves and Modular Forms
  Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
• C. Lectures on Elliptic Curves
  Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
• D. Hasse bound for elliptic curves
  The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
• E. modularity theorem for elliptic curves over Q
  The modularity theorem for elliptic curves over Q is a landmark result in number theory stating that every elliptic curve defined over the rational numbers corresponds to a modular form, a fact central to the proof of Fermat’s Last Theorem.
• F. None of above. chosen