K12a572
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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^4+9 t^3-21 t^2+35 t-41+35 t^{-1} -21 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-7 z^4+1 }[/math] |
| Determinant | 175 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-10 z^4 a^{-2} -4 z^4 a^{-4} +3 z^4 a^{-6} +4 z^4-9 z^2 a^{-2} +2 z^2 a^{-4} +2 z^2 a^{-6} +5 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +11 z^{10} a^{-4} +6 z^{10} a^{-6} +6 z^9 a^{-1} +7 z^9 a^{-3} +9 z^9 a^{-5} +8 z^9 a^{-7} -7 z^8 a^{-2} -26 z^8 a^{-4} -7 z^8 a^{-6} +7 z^8 a^{-8} +5 z^8+3 a z^7-13 z^7 a^{-1} -29 z^7 a^{-3} -31 z^7 a^{-5} -14 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-3 z^6 a^{-2} +22 z^6 a^{-4} -3 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -12 z^6-8 a z^5+10 z^5 a^{-1} +39 z^5 a^{-3} +32 z^5 a^{-5} +2 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4+18 z^4 a^{-2} +4 z^4 a^{-4} +5 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} +9 z^4+5 a z^3-4 z^3 a^{-1} -14 z^3 a^{-3} -7 z^3 a^{-5} +3 z^3 a^{-7} +5 z^3 a^{-9} +2 a^2 z^2-15 z^2 a^{-2} -8 z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -6 z^2-a z-z a^{-1} -2 z a^{-5} -3 z a^{-7} -z a^{-9} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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