K12a958
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-9 q^{-1} +17 q^{-2} -23 q^{-3} +29 q^{-4} -31 q^{-5} +29 q^{-6} -24 q^{-7} +16 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+25 t^2-39 t+45-39 t^{-1} +25 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+z^8 a^6+4 z^6 a^6+5 z^4 a^6+z^2 a^6-2 a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+6 z^2 a^4+3 a^4-z^6 a^2-3 z^4 a^2-2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-11 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+11 z^8 a^{10}-16 z^6 a^{10}+7 z^4 a^{10}-z^2 a^{10}+12 z^9 a^9-21 z^7 a^9+14 z^5 a^9-z^3 a^9-z a^9+9 z^{10} a^8-13 z^8 a^8+3 z^6 a^8+5 z^4 a^8+3 z^{11} a^7+12 z^9 a^7-49 z^7 a^7+54 z^5 a^7-17 z^3 a^7-z a^7+16 z^{10} a^6-44 z^8 a^6+39 z^6 a^6-11 z^4 a^6-2 z^2 a^6+2 a^6+3 z^{11} a^5+7 z^9 a^5-42 z^7 a^5+48 z^5 a^5-19 z^3 a^5+7 z^{10} a^4-16 z^8 a^4+3 z^6 a^4+8 z^4 a^4-8 z^2 a^4+3 a^4+7 z^9 a^3-21 z^7 a^3+17 z^5 a^3-6 z^3 a^3+z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-4 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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