K12a955
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+9 q^6-16 q^5+23 q^4-28 q^3+30 q^2-28 q+24-16 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-44 t+57-44 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-4 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -z^4+a^2 z^2-2 z^2 a^{-2} +z^2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +11 z^{10} a^{-2} +17 z^{10} a^{-4} +6 z^{10} a^{-6} +19 z^9 a^{-1} +19 z^9 a^{-3} +4 z^9 a^{-5} +4 z^9 a^{-7} -10 z^8 a^{-2} -53 z^8 a^{-4} -22 z^8 a^{-6} +z^8 a^{-8} +20 z^8+15 a z^7-41 z^7 a^{-1} -88 z^7 a^{-3} -49 z^7 a^{-5} -17 z^7 a^{-7} +9 a^2 z^6-38 z^6 a^{-2} +35 z^6 a^{-4} +22 z^6 a^{-6} -4 z^6 a^{-8} -38 z^6+4 a^3 z^5-18 a z^5+24 z^5 a^{-1} +96 z^5 a^{-3} +74 z^5 a^{-5} +24 z^5 a^{-7} +a^4 z^4-6 a^2 z^4+47 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} +5 z^4 a^{-8} +23 z^4-a^3 z^3+5 a z^3-8 z^3 a^{-1} -38 z^3 a^{-3} -37 z^3 a^{-5} -13 z^3 a^{-7} +a^2 z^2-14 z^2 a^{-2} -8 z^2 a^{-4} -3 z^2 a^{-6} -2 z^2 a^{-8} -6 z^2+2 z a^{-1} +6 z a^{-3} +6 z a^{-5} +2 z a^{-7} +1 }[/math] |
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