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: SL(2,ℤ) | Statement: [PSL(2,ℤ), commensurableWith, SL(2,ℤ)]

Target entity: SL(2,ℤ)
Context triple: [PSL(2,ℤ), commensurableWith, SL(2,ℤ)]

• A. SL(2,ℤ) chosen
  SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
• B. PSL(2,ℤ/Nℤ)
  PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
• C. SL(2,C)
  SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
• D. modular group PSL(2,Z)
  The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
• E. PSL(2,7)
  PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: commensurableWith
Context triple: [PSL(2,ℤ), commensurableWith, SL(2,ℤ)]

• A. isCommutative
  Indicates that the result of applying an operation to two entities does not depend on their order (i.e., a ∘ b = b ∘ a).
• B. isProportionalTo
  Indicates that one quantity varies in constant ratio to another, so when one changes, the other changes by a fixed multiplicative factor.
• C. equivalentIn
  Indicates that two entities are considered logically or functionally the same in meaning, status, or effect within a given context.
• D. isEquiconsistentWith
  Indicates that two formal theories or systems have the same consistency strength, such that if one is consistent then the other is also consistent, and if one is inconsistent then so is the other.
• E. isQuotientOf
  Indicates that one quantity is the result of dividing another quantity by a specified divisor.
• F. None of above. chosen