K12a88
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-23 q^6+35 q^5-43 q^4+47 q^3-44 q^2+36 q-25+14 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-30 t^2+65 t-83+65 t^{-1} -30 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^4+z^2+1 }[/math] |
| Determinant | 291 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-9 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-9 z^2 a^{-2} +10 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +3 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +12 z^{10} a^{-2} +22 z^{10} a^{-4} +10 z^{10} a^{-6} +18 z^9 a^{-1} +38 z^9 a^{-3} +34 z^9 a^{-5} +14 z^9 a^{-7} +6 z^8 a^{-2} -8 z^8 a^{-4} +10 z^8 a^{-6} +11 z^8 a^{-8} +13 z^8+5 a z^7-31 z^7 a^{-1} -93 z^7 a^{-3} -79 z^7 a^{-5} -17 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-56 z^6 a^{-2} -68 z^6 a^{-4} -56 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} -23 z^6-6 a z^5+19 z^5 a^{-1} +67 z^5 a^{-3} +49 z^5 a^{-5} -z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+57 z^4 a^{-2} +80 z^4 a^{-4} +55 z^4 a^{-6} +13 z^4 a^{-8} -z^4 a^{-10} +17 z^4+2 a z^3-8 z^3 a^{-1} -20 z^3 a^{-3} -6 z^3 a^{-5} +8 z^3 a^{-7} +4 z^3 a^{-9} -25 z^2 a^{-2} -33 z^2 a^{-4} -20 z^2 a^{-6} -4 z^2 a^{-8} -8 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} -2 z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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