K12n753
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+7 q^{10}-12 q^9+15 q^8-18 q^7+17 q^6-14 q^5+11 q^4-5 q^3+2 q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+11 t^2-24 t+31-24 t^{-1} +11 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-6} -z^6 a^{-8} +2 z^4 a^{-4} -z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +4 z^2 a^{-4} +2 z^2 a^{-6} -6 z^2 a^{-8} +2 z^2 a^{-10} +2 a^{-4} +2 a^{-6} -5 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-8} +2 z^{10} a^{-10} +4 z^9 a^{-7} +9 z^9 a^{-9} +5 z^9 a^{-11} +3 z^8 a^{-6} +z^8 a^{-8} +3 z^8 a^{-10} +5 z^8 a^{-12} +z^7 a^{-5} -8 z^7 a^{-7} -24 z^7 a^{-9} -12 z^7 a^{-11} +3 z^7 a^{-13} -2 z^6 a^{-6} -3 z^6 a^{-8} -15 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} +3 z^5 a^{-5} +16 z^5 a^{-7} +33 z^5 a^{-9} +12 z^5 a^{-11} -8 z^5 a^{-13} +3 z^4 a^{-4} +2 z^4 a^{-6} +14 z^4 a^{-10} +10 z^4 a^{-12} -3 z^4 a^{-14} -3 z^3 a^{-5} -15 z^3 a^{-7} -28 z^3 a^{-9} -11 z^3 a^{-11} +5 z^3 a^{-13} -5 z^2 a^{-4} +7 z^2 a^{-8} -4 z^2 a^{-10} -4 z^2 a^{-12} +2 z^2 a^{-14} -z a^{-5} +6 z a^{-7} +12 z a^{-9} +4 z a^{-11} -z a^{-13} +2 a^{-4} -2 a^{-6} -5 a^{-8} -2 a^{-10} }[/math] |
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