K13n4047
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Polynomial invariants
| Jones polynomial | Data:K13n4047/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+27 t^2-38 t+41-38 t^{-1} +27 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13n4047/Conway Polynomial |
| Determinant | 197 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +3 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -2 z^4 a^{-2} +2 z^4 a^{-4} +5 z^4 a^{-6} -4 z^4 a^{-8} +3 z^2 a^{-4} +2 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +10 z^{10} a^{-4} +20 z^{10} a^{-6} +10 z^{10} a^{-8} +10 z^9 a^{-3} +10 z^9 a^{-5} +8 z^9 a^{-7} +8 z^9 a^{-9} +5 z^8 a^{-2} -21 z^8 a^{-4} -58 z^8 a^{-6} -30 z^8 a^{-8} +2 z^8 a^{-10} +z^7 a^{-1} -27 z^7 a^{-3} -60 z^7 a^{-5} -56 z^7 a^{-7} -24 z^7 a^{-9} -13 z^6 a^{-2} -3 z^6 a^{-4} +46 z^6 a^{-6} +38 z^6 a^{-8} +2 z^6 a^{-10} -2 z^5 a^{-1} +17 z^5 a^{-3} +63 z^5 a^{-5} +81 z^5 a^{-7} +42 z^5 a^{-9} +5 z^5 a^{-11} +9 z^4 a^{-2} +14 z^4 a^{-4} -4 z^4 a^{-6} -10 z^4 a^{-8} +z^4 a^{-12} +z^3 a^{-1} -5 z^3 a^{-3} -25 z^3 a^{-5} -38 z^3 a^{-7} -25 z^3 a^{-9} -6 z^3 a^{-11} -2 z^2 a^{-2} -9 z^2 a^{-4} -7 z^2 a^{-6} -z^2 a^{-8} -2 z^2 a^{-10} -z^2 a^{-12} +z a^{-3} +2 z a^{-5} +5 z a^{-7} +5 z a^{-9} +z a^{-11} +3 a^{-4} +2 a^{-6} }[/math] |
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