K12a860
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +14 q^{-2} -18 q^{-3} +22 q^{-4} -23 q^{-5} +21 q^{-6} -17 q^{-7} +11 q^{-8} -6 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+20 t^2-28 t+31-28 t^{-1} +20 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-4 z^2 a^8-a^8+z^8 a^6+5 z^6 a^6+9 z^4 a^6+7 z^2 a^6+a^6+z^8 a^4+4 z^6 a^4+4 z^4 a^4+z^2 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+3 z^6 a^{12}-6 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-10 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+6 z^8 a^{10}-11 z^6 a^{10}+8 z^4 a^{10}+6 z^9 a^9-11 z^7 a^9+8 z^5 a^9+4 z^3 a^9-2 z a^9+5 z^{10} a^8-11 z^8 a^8+16 z^6 a^8-12 z^4 a^8+7 z^2 a^8-a^8+2 z^{11} a^7+3 z^9 a^7-17 z^7 a^7+23 z^5 a^7-11 z^3 a^7+10 z^{10} a^6-33 z^8 a^6+48 z^6 a^6-41 z^4 a^6+14 z^2 a^6-a^6+2 z^{11} a^5+3 z^9 a^5-21 z^7 a^5+21 z^5 a^5-10 z^3 a^5+z a^5+5 z^{10} a^4-12 z^8 a^4+4 z^6 a^4-2 z^4 a^4+3 z^2 a^4+6 z^9 a^3-19 z^7 a^3+14 z^5 a^3-2 z^3 a^3+z a^3+4 z^8 a^2-14 z^6 a^2+13 z^4 a^2-2 z^2 a^2-a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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