K12a549
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-10 q^6+14 q^5-16 q^4+17 q^3-16 q^2+12 q-8+5 q^{-1} -2 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^2-4 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +z^2 a^{-8} +a^2-2 a^{-2} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} +z^9 a^{-3} +2 z^9 a^{-5} +4 z^9 a^{-7} -2 z^8 a^{-2} -17 z^8 a^{-4} -8 z^8 a^{-6} +4 z^8 a^{-8} +3 z^8+2 a z^7-8 z^7 a^{-1} -8 z^7 a^{-3} -11 z^7 a^{-5} -10 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-7 z^6 a^{-2} +28 z^6 a^{-4} +14 z^6 a^{-6} -10 z^6 a^{-8} +z^6 a^{-10} -9 z^6-6 a z^5+8 z^5 a^{-1} +15 z^5 a^{-3} +20 z^5 a^{-5} +10 z^5 a^{-7} -9 z^5 a^{-9} -4 a^2 z^4+19 z^4 a^{-2} -16 z^4 a^{-4} -15 z^4 a^{-6} +5 z^4 a^{-8} -3 z^4 a^{-10} +8 z^4+3 a z^3-6 z^3 a^{-1} -6 z^3 a^{-3} -12 z^3 a^{-5} -9 z^3 a^{-7} +6 z^3 a^{-9} +4 a^2 z^2-13 z^2 a^{-2} +4 z^2 a^{-4} +5 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} -5 z^2+2 z a^{-1} +2 z a^{-3} +2 z a^{-5} +2 z a^{-7} -a^2+2 a^{-2} - a^{-6} +1 }[/math] |
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