K12a799
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+22 q^5-26 q^4+28 q^3-25 q^2+20 q-13+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+42 t-57+42 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4+1 }[/math] |
| Determinant | 175 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} -2 z^4 a^{-6} -2 z^4+a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -3 z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +11 z^{10} a^{-4} +7 z^{10} a^{-6} +4 z^9 a^{-1} +4 z^9 a^{-3} +10 z^9 a^{-5} +10 z^9 a^{-7} -4 z^8 a^{-2} -29 z^8 a^{-4} -13 z^8 a^{-6} +8 z^8 a^{-8} +4 z^8+3 a z^7-11 z^7 a^{-3} -39 z^7 a^{-5} -27 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+8 z^6 a^{-2} +41 z^6 a^{-4} +6 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -5 z^6-8 a z^5-14 z^5 a^{-1} +12 z^5 a^{-3} +53 z^5 a^{-5} +26 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4-19 z^4 a^{-2} -29 z^4 a^{-4} +3 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} -5 z^4+7 a z^3+12 z^3 a^{-1} -7 z^3 a^{-3} -26 z^3 a^{-5} -11 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2+13 z^2 a^{-2} +10 z^2 a^{-4} -z^2 a^{-6} -3 z^2 a^{-8} +8 z^2-2 a z-3 z a^{-1} +z a^{-3} +3 z a^{-5} +z a^{-7} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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