K12a976
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-13+25 q^{-1} -35 q^{-2} +43 q^{-3} -45 q^{-4} +41 q^{-5} -33 q^{-6} +22 q^{-7} -11 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-25 t^2+66 t-89+66 t^{-1} -25 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 279 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+4 z^2 a^8+3 a^8-6 z^4 a^6-9 z^2 a^6-4 a^6+3 z^6 a^4+7 z^4 a^4+8 z^2 a^4+2 a^4+z^6 a^2-z^4 a^2-z^2 a^2+a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-11 z^6 a^{10}+11 z^4 a^{10}-5 z^2 a^{10}+a^{10}+8 z^9 a^9-19 z^7 a^9+15 z^5 a^9-5 z^3 a^9+z a^9+9 z^{10} a^8-12 z^8 a^8-11 z^6 a^8+24 z^4 a^8-15 z^2 a^8+3 a^8+4 z^{11} a^7+19 z^9 a^7-71 z^7 a^7+69 z^5 a^7-29 z^3 a^7+5 z a^7+25 z^{10} a^6-41 z^8 a^6-11 z^6 a^6+41 z^4 a^6-23 z^2 a^6+4 a^6+4 z^{11} a^5+37 z^9 a^5-107 z^7 a^5+88 z^5 a^5-30 z^3 a^5+5 z a^5+16 z^{10} a^4-2 z^8 a^4-50 z^6 a^4+50 z^4 a^4-17 z^2 a^4+2 a^4+26 z^9 a^3-43 z^7 a^3+25 z^5 a^3-7 z^3 a^3+2 z a^3+23 z^8 a^2-34 z^6 a^2+20 z^4 a^2-4 z^2 a^2-a^2+13 z^7 a-11 z^5 a+2 z^3 a+5 z^6-2 z^4+z^5 a^{-1} }[/math] |
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