K12a168
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+2 q-4+8 q^{-1} -10 q^{-2} +14 q^{-3} -15 q^{-4} +14 q^{-5} -12 q^{-6} +9 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-11 t^2+22 t-27+22 t^{-1} -11 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+3 z^2 a^6+a^6+z^6 a^4+2 z^4 a^4-2 a^4+z^6 a^2+4 z^4 a^2+7 z^2 a^2+5 a^2-z^4-3 z^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+12 z^4 a^{10}-3 z^2 a^{10}+4 z^9 a^9-15 z^7 a^9+14 z^5 a^9-5 z^3 a^9+2 z a^9+3 z^{10} a^8-9 z^8 a^8+5 z^6 a^8-2 z^4 a^8+3 z^2 a^8-a^8+z^{11} a^7+2 z^9 a^7-17 z^7 a^7+25 z^5 a^7-17 z^3 a^7+4 z a^7+5 z^{10} a^6-19 z^8 a^6+30 z^6 a^6-24 z^4 a^6+8 z^2 a^6-a^6+z^{11} a^5-5 z^7 a^5+12 z^5 a^5-10 z^3 a^5+3 z a^5+2 z^{10} a^4-5 z^8 a^4+11 z^6 a^4-11 z^4 a^4+7 z^2 a^4-2 a^4+2 z^9 a^3-2 z^7 a^3+3 z^5 a^3-4 z^3 a^3+4 z a^3+2 z^8 a^2-6 z^4 a^2+9 z^2 a^2-5 a^2+2 z^7 a-z^5 a-5 z^3 a+4 z a+2 z^6-5 z^4+4 z^2-2+z^5 a^{-1} -3 z^3 a^{-1} +2 z a^{-1} }[/math] |
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