K12a1136
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-12 q^6+17 q^5-22 q^4+23 q^3-21 q^2+18 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-18 t^2+29 t-33+29 t^{-1} -18 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-10 z^4-3 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-9 z^4 a^{-2} -9 z^4 a^{-4} +4 z^4 a^{-6} +4 z^4-6 z^2 a^{-2} -7 z^2 a^{-4} +5 z^2 a^{-6} +5 z^2-3 a^{-4} +2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +6 z^9 a^{-3} +6 z^9 a^{-5} +5 z^9 a^{-7} -10 z^8 a^{-4} +5 z^8 a^{-8} +5 z^8+3 a z^7-10 z^7 a^{-1} -13 z^7 a^{-3} -13 z^7 a^{-5} -10 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-8 z^6 a^{-2} +12 z^6 a^{-4} -8 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -13 z^6-8 a z^5+8 z^5 a^{-1} +10 z^5 a^{-3} +9 z^5 a^{-5} +7 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+10 z^4 a^{-2} -13 z^4 a^{-4} +6 z^4 a^{-6} +11 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+5 a z^3-5 z^3 a^{-1} -2 z^3 a^{-3} -z^3 a^{-5} -4 z^3 a^{-7} +5 z^3 a^{-9} +2 a^2 z^2-7 z^2 a^{-2} +11 z^2 a^{-4} +2 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2 a^{-10} -7 z^2+2 z a^{-5} +z a^{-7} -z a^{-9} -3 a^{-4} -2 a^{-6} +2 }[/math] |
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