K12a997
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-18 q^6+26 q^5-32 q^4+34 q^3-32 q^2+26 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-26 t^2+44 t-51+44 t^{-1} -26 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-6 z^4-2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-4 z^2 a^{-2} -4 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +17 z^{10} a^{-4} +8 z^{10} a^{-6} +12 z^9 a^{-1} +14 z^9 a^{-3} +12 z^9 a^{-5} +10 z^9 a^{-7} -14 z^8 a^{-2} -41 z^8 a^{-4} -10 z^8 a^{-6} +8 z^8 a^{-8} +9 z^8+4 a z^7-32 z^7 a^{-1} -55 z^7 a^{-3} -42 z^7 a^{-5} -19 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-4 z^6 a^{-2} +41 z^6 a^{-4} +4 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -23 z^6-8 a z^5+32 z^5 a^{-1} +68 z^5 a^{-3} +50 z^5 a^{-5} +14 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+23 z^4 a^{-2} -16 z^4 a^{-4} -7 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +19 z^4+a z^3-13 z^3 a^{-1} -27 z^3 a^{-3} -28 z^3 a^{-5} -11 z^3 a^{-7} +4 z^3 a^{-9} -11 z^2 a^{-2} +4 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -9 z^2+z a^{-1} +3 z a^{-3} +5 z a^{-5} +3 z a^{-7} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
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