K12a684
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-12 q^6+17 q^5-20 q^4+21 q^3-20 q^2+15 q-10+6 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+32 t-39+32 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-6 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-z^2 a^{-2} -3 z^2 a^{-6} +z^2 a^{-8} -4 z^2+2 a^2- a^{-2} + a^{-4} - a^{-6} + a^{-8} -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} +2 z^9 a^{-3} +4 z^9 a^{-5} +5 z^9 a^{-7} +z^8 a^{-2} -9 z^8 a^{-4} -2 z^8 a^{-6} +5 z^8 a^{-8} +3 z^8+2 a z^7-4 z^7 a^{-1} +z^7 a^{-3} -7 z^7 a^{-5} -11 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-6 z^6 a^{-2} +14 z^6 a^{-4} -z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -6 z^6-5 a z^5+2 z^5 a^{-1} -8 z^5 a^{-3} +4 z^5 a^{-5} +11 z^5 a^{-7} -8 z^5 a^{-9} -4 a^2 z^4+8 z^4 a^{-2} -12 z^4 a^{-4} +11 z^4 a^{-8} -3 z^4 a^{-10} +2 z^4+2 a z^3-4 z^3 a^{-1} +8 z^3 a^{-3} -9 z^3 a^{-7} +5 z^3 a^{-9} +5 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2 a^{-10} +z^2+a z+3 z a^{-1} -z a^{-3} -z a^{-5} +2 z a^{-7} -2 a^2+ a^{-2} + a^{-4} + a^{-6} + a^{-8} -1 }[/math] |
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