K12a1077
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-8+14 q^{-1} -20 q^{-2} +25 q^{-3} -26 q^{-4} +25 q^{-5} -20 q^{-6} +14 q^{-7} -9 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-16 t^2+40 t-53+40 t^{-1} -16 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8-a^8+z^6 a^6+2 z^4 a^6+3 z^2 a^6+a^6+z^6 a^4-z^2 a^4+z^6 a^2+2 z^4 a^2+3 z^2 a^2+a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+z^3 a^{11}+4 z^8 a^{10}-13 z^6 a^{10}+8 z^4 a^{10}-z^2 a^{10}+8 z^9 a^9-30 z^7 a^9+32 z^5 a^9-15 z^3 a^9+4 z a^9+8 z^{10} a^8-28 z^8 a^8+29 z^6 a^8-14 z^4 a^8+5 z^2 a^8-a^8+3 z^{11} a^7+4 z^9 a^7-45 z^7 a^7+69 z^5 a^7-36 z^3 a^7+6 z a^7+15 z^{10} a^6-54 z^8 a^6+71 z^6 a^6-38 z^4 a^6+8 z^2 a^6-a^6+3 z^{11} a^5+4 z^9 a^5-31 z^7 a^5+47 z^5 a^5-24 z^3 a^5+3 z a^5+7 z^{10} a^4-14 z^8 a^4+17 z^6 a^4-14 z^4 a^4+5 z^2 a^4+8 z^9 a^3-10 z^7 a^3+2 z^5 a^3+z a^3+8 z^8 a^2-8 z^6 a^2-4 z^4 a^2+5 z^2 a^2-a^2+7 z^7 a-10 z^5 a+3 z^3 a+4 z^6-6 z^4+2 z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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