K12a85
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +11 q^{-2} -16 q^{-3} +21 q^{-4} -22 q^{-5} +22 q^{-6} -18 q^{-7} +13 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-28 t+31-28 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+8 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-6 z^2 a^8-4 a^8+z^8 a^6+5 z^6 a^6+10 z^4 a^6+11 z^2 a^6+5 a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+7 z^2 a^4+a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-10 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+7 z^8 a^{10}-9 z^6 a^{10}+4 z^4 a^{10}-z^2 a^{10}+6 z^9 a^9-5 z^7 a^9-2 z^5 a^9+4 z^3 a^9-z a^9+4 z^{10} a^8-3 z^8 a^8+6 z^6 a^8-17 z^4 a^8+16 z^2 a^8-4 a^8+z^{11} a^7+9 z^9 a^7-28 z^7 a^7+37 z^5 a^7-27 z^3 a^7+8 z a^7+7 z^{10} a^6-17 z^8 a^6+19 z^6 a^6-19 z^4 a^6+14 z^2 a^6-5 a^6+z^{11} a^5+7 z^9 a^5-31 z^7 a^5+42 z^5 a^5-26 z^3 a^5+5 z a^5+3 z^{10} a^4-4 z^8 a^4-11 z^6 a^4+20 z^4 a^4-10 z^2 a^4+a^4+4 z^9 a^3-13 z^7 a^3+10 z^5 a^3-z^3 a^3+3 z^8 a^2-12 z^6 a^2+14 z^4 a^2-6 z^2 a^2+a^2+z^7 a-4 z^5 a+4 z^3 a-z a }[/math] |
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