K12a1145
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+4 q^7-7 q^6+9 q^5-11 q^4+12 q^3-11 q^2+9 q-6+4 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+6 t^3-10 t^2+14 t-15+14 t^{-1} -10 t^{-2} +6 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-10 z^6-14 z^4-4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -6 z^6 a^{-2} -6 z^6 a^{-4} +z^6 a^{-6} +z^6-12 z^4 a^{-2} -12 z^4 a^{-4} +5 z^4 a^{-6} +5 z^4-9 z^2 a^{-2} -9 z^2 a^{-4} +7 z^2 a^{-6} +7 z^2-2 a^{-2} -2 a^{-4} +2 a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +3 z^9 a^{-1} -2 z^9 a^{-3} -3 z^9 a^{-5} +2 z^9 a^{-7} -6 z^8 a^{-2} -20 z^8 a^{-4} -9 z^8 a^{-6} +2 z^8 a^{-8} +3 z^8+2 a z^7-12 z^7 a^{-1} -2 z^7 a^{-3} +4 z^7 a^{-5} -6 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6+z^6 a^{-2} +42 z^6 a^{-4} +22 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} -12 z^6-7 a z^5+16 z^5 a^{-1} +8 z^5 a^{-3} +z^5 a^{-5} +9 z^5 a^{-7} -7 z^5 a^{-9} -4 a^2 z^4+14 z^4 a^{-2} -37 z^4 a^{-4} -26 z^4 a^{-6} +2 z^4 a^{-8} -4 z^4 a^{-10} +15 z^4+4 a z^3-9 z^3 a^{-1} +z^3 a^{-3} -2 z^3 a^{-5} -10 z^3 a^{-7} +6 z^3 a^{-9} +3 a^2 z^2-12 z^2 a^{-2} +18 z^2 a^{-4} +11 z^2 a^{-6} -z^2 a^{-8} +4 z^2 a^{-10} -11 z^2-z a^{-3} +z a^{-5} +z a^{-7} -z a^{-9} +2 a^{-2} -2 a^{-4} -2 a^{-6} +3 }[/math] |
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