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: Klein quartic | Statement: [PSL(2,7), fullAutomorphismGroupOf, Klein quartic]

Target entity: Klein quartic
Context triple: [PSL(2,7), fullAutomorphismGroupOf, Klein quartic]

• A. 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.
• B. Clebsch
  Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
• C. Kummer surfaces
  Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
• D. 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.
• E. Fermat surface
  A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: fullAutomorphismGroupOf
Context triple: [PSL(2,7), fullAutomorphismGroupOf, Klein quartic]

• A. automorphismGroupIsomorphicTo
  Indicates that the automorphism group of one structure is isomorphic, as a group, to the automorphism group of another structure.
• B. automorphismGroupOrder
  Indicates the size of the group of all structure-preserving bijections (automorphisms) of an object under composition.
• C. outerAutomorphismGroup
  Indicates that one group is the group of all outer automorphisms (automorphisms modulo inner automorphisms) of another group.
• D. hasOuterAutomorphismGroupOrder
  Indicates the relationship that specifies the order (size) of the outer automorphism group associated with a given mathematical structure.
• E. hasAutomorphism
  Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
• F. None of above. chosen