K12a1160
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+5 q^7-9 q^6+12 q^5-16 q^4+17 q^3-16 q^2+14 q-9+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+28 t-39+28 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4-4 z^2+1 }[/math] |
| Determinant | 111 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -3 z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-3 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-8} +z^2-2 a^{-4} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +5 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-1} +3 z^9 a^{-3} +z^9 a^{-5} +3 z^9 a^{-7} -5 z^8 a^{-2} -16 z^8 a^{-4} -3 z^8 a^{-6} +3 z^8 a^{-8} +5 z^8+3 a z^7-16 z^7 a^{-1} -17 z^7 a^{-3} -9 z^7 a^{-5} -9 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6-7 z^6 a^{-2} +22 z^6 a^{-4} +z^6 a^{-6} -9 z^6 a^{-8} +z^6 a^{-10} -17 z^6-9 a z^5+16 z^5 a^{-1} +27 z^5 a^{-3} +25 z^5 a^{-5} +17 z^5 a^{-7} -6 z^5 a^{-9} -3 a^2 z^4+22 z^4 a^{-2} -7 z^4 a^{-4} +5 z^4 a^{-6} +10 z^4 a^{-8} -4 z^4 a^{-10} +17 z^4+4 a z^3-6 z^3 a^{-1} -12 z^3 a^{-3} -28 z^3 a^{-5} -22 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-11 z^2 a^{-2} +2 z^2 a^{-4} -8 z^2 a^{-6} -7 z^2 a^{-8} +4 z^2 a^{-10} -9 z^2+4 z a^{-3} +12 z a^{-5} +8 z a^{-7} -2 a^{-4} + a^{-8} +2 }[/math] |
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