K12a113
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-17 q^6+26 q^5-32 q^4+35 q^3-33 q^2+27 q-19+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+48 t-59+48 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 219 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +3 z^6 a^{-4} +z^6-13 z^4 a^{-2} +11 z^4 a^{-4} -3 z^4 a^{-6} +3 z^4-17 z^2 a^{-2} +17 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +5 z^2-9 a^{-2} +10 a^{-4} -5 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +5 z^{10} a^{-2} +9 z^{10} a^{-4} +4 z^{10} a^{-6} +10 z^9 a^{-1} +23 z^9 a^{-3} +20 z^9 a^{-5} +7 z^9 a^{-7} +17 z^8 a^{-2} +17 z^8 a^{-4} +16 z^8 a^{-6} +7 z^8 a^{-8} +9 z^8+4 a z^7-13 z^7 a^{-1} -43 z^7 a^{-3} -32 z^7 a^{-5} -2 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-65 z^6 a^{-2} -84 z^6 a^{-4} -53 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -19 z^6-7 a z^5-z^5 a^{-1} +12 z^5 a^{-3} -4 z^5 a^{-5} -19 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+74 z^4 a^{-2} +98 z^4 a^{-4} +55 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +18 z^4+4 a z^3+5 z^3 a^{-1} +12 z^3 a^{-3} +26 z^3 a^{-5} +22 z^3 a^{-7} +7 z^3 a^{-9} +a^2 z^2-42 z^2 a^{-2} -50 z^2 a^{-4} -26 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -12 z^2-a z-2 z a^{-1} -5 z a^{-3} -9 z a^{-5} -7 z a^{-7} -2 z a^{-9} +9 a^{-2} +10 a^{-4} +5 a^{-6} + a^{-8} +4 }[/math] |
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