K12a187
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-11+19 q^{-1} -26 q^{-2} +31 q^{-3} -32 q^{-4} +29 q^{-5} -22 q^{-6} +15 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-16 t^2+49 t-69+49 t^{-1} -16 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^4+3 z^2+1 }[/math] |
| Determinant | 203 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+3 z^2 a^8+a^8-3 z^4 a^6-z^2 a^6+a^6+z^6 a^4-z^4 a^4-2 z^2 a^4-2 a^4+z^6 a^2+z^4 a^2+3 z^2 a^2+2 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+10 z^4 a^{10}-4 z^2 a^{10}+a^{10}+5 z^9 a^9-14 z^7 a^9+11 z^5 a^9-4 z^3 a^9+z a^9+5 z^{10} a^8-9 z^8 a^8-z^6 a^8+6 z^4 a^8-4 z^2 a^8+a^8+2 z^{11} a^7+10 z^9 a^7-42 z^7 a^7+51 z^5 a^7-28 z^3 a^7+5 z a^7+13 z^{10} a^6-26 z^8 a^6+11 z^6 a^6+3 z^4 a^6-a^6+2 z^{11} a^5+19 z^9 a^5-56 z^7 a^5+53 z^5 a^5-19 z^3 a^5+2 z a^5+8 z^{10} a^4+z^8 a^4-23 z^6 a^4+14 z^4 a^4+4 z^2 a^4-2 a^4+14 z^9 a^3-18 z^7 a^3+3 z^5 a^3+2 z^3 a^3+15 z^8 a^2-20 z^6 a^2+3 z^4 a^2+4 z^2 a^2-2 a^2+11 z^7 a-13 z^5 a+2 z^3 a+5 z^6-4 z^4+z^5 a^{-1} }[/math] |
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