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: Hurwitz curve | Statement: [Hurwitz bound on automorphism groups of curves, relatedConcept, Hurwitz curve]

Target entity: Hurwitz curve
Context triple: [Hurwitz bound on automorphism groups of curves, relatedConcept, Hurwitz curve]

• A. Hurwitz space
  A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
• B. Klein quartic chosen
  The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
• C. Fermat curve
  A Fermat curve is an algebraic curve defined by an equation of the form \(x^n + y^n = 1\), studied in number theory and algebraic geometry for its rich arithmetic and geometric properties.
• D. Hurwitz bound on automorphism groups of curves
  The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
• E. Riemann–Hurwitz formula
  The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.