K12a1164
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+7 q^8-11 q^7+14 q^6-16 q^5+16 q^4-14 q^3+10 q^2-7 q+4- q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+13 t^2-22 t+27-22 t^{-1} +13 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-11 z^4-6 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} -7 z^4 a^{-4} -2 z^4 a^{-6} +z^4 a^{-8} +z^4-6 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-8} +4 z^2-4 a^{-2} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10} a^{-6} +z^9 a^{-1} -4 z^9 a^{-3} +z^9 a^{-5} +6 z^9 a^{-7} -2 z^8 a^{-2} -15 z^8 a^{-4} -4 z^8 a^{-6} +8 z^8 a^{-8} +z^8-4 z^7 a^{-1} +13 z^7 a^{-3} -4 z^7 a^{-5} -13 z^7 a^{-7} +8 z^7 a^{-9} -6 z^6 a^{-2} +25 z^6 a^{-4} +3 z^6 a^{-6} -15 z^6 a^{-8} +6 z^6 a^{-10} -7 z^6+2 z^5 a^{-1} -35 z^5 a^{-3} -4 z^5 a^{-5} +18 z^5 a^{-7} -12 z^5 a^{-9} +3 z^5 a^{-11} +17 z^4 a^{-2} -30 z^4 a^{-4} -8 z^4 a^{-6} +14 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +17 z^4+6 z^3 a^{-1} +38 z^3 a^{-3} +4 z^3 a^{-5} -18 z^3 a^{-7} +8 z^3 a^{-9} -2 z^3 a^{-11} -13 z^2 a^{-2} +15 z^2 a^{-4} +z^2 a^{-6} -6 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} -16 z^2-4 z a^{-1} -10 z a^{-3} -2 z a^{-5} +4 z a^{-7} +4 a^{-2} + a^{-8} +4 }[/math] |
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