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: automorphism group of the Leech lattice | Statement: [Leech lattice, hasAutomorphismGroup, automorphism group of the Leech lattice]

Target entity: automorphism group of the Leech lattice
Context triple: [Leech lattice, hasAutomorphismGroup, automorphism group of the Leech lattice]

• A. Leech lattice
  The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
• B. Conway–Norton collaboration
  The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
• C. Conway’s topograph
  Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
• D. Conway groups chosen
  Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
• E. The Classical Groups: Their Invariants and Representations
  The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasAutomorphismGroup
Context triple: [Leech lattice, hasAutomorphismGroup, automorphism group of the Leech lattice]

• A. hasIsometryGroup chosen
  Indicates that one entity possesses or is associated with a particular isometry group describing all distance-preserving transformations of that entity.
• B. usesSymmetryGroup
  Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
• C. isNonAbelian
  Indicates that the operation or structure in question does not satisfy commutativity, so the order of applying the operation matters.
• D. isMaximallySymmetric
  Indicates that the subject exhibits the highest possible degree of symmetry allowed by the relevant structure, constraints, or context.
• E. hasAdditiveGroupIsomorphicTo
  Indicates that the additive group structure of one algebraic object is isomorphic (structure-preserving bijection exists) to the additive group structure of another.
• F. None of above.