K12a594
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-5+9 q^{-1} -12 q^{-2} +14 q^{-3} -15 q^{-4} +14 q^{-5} -10 q^{-6} +8 q^{-7} -5 q^{-8} +2 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^8-3 z^2 a^8-3 a^8+z^6 a^6+4 z^4 a^6+7 z^2 a^6+5 a^6+z^6 a^4+2 z^4 a^4-2 a^4+z^6 a^2+3 z^4 a^2+3 z^2 a^2+a^2-z^4-2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+7 z^3 a^{11}-3 z a^{11}+2 z^8 a^{10}-8 z^6 a^{10}+7 z^4 a^{10}-z^2 a^{10}+3 z^9 a^9-12 z^7 a^9+13 z^5 a^9-7 z^3 a^9+2 z a^9+3 z^{10} a^8-13 z^8 a^8+23 z^6 a^8-30 z^4 a^8+20 z^2 a^8-3 a^8+z^{11} a^7+2 z^9 a^7-23 z^7 a^7+47 z^5 a^7-40 z^3 a^7+10 z a^7+6 z^{10} a^6-28 z^8 a^6+55 z^6 a^6-55 z^4 a^6+28 z^2 a^6-5 a^6+z^{11} a^5+3 z^9 a^5-25 z^7 a^5+54 z^5 a^5-40 z^3 a^5+7 z a^5+3 z^{10} a^4-9 z^8 a^4+14 z^6 a^4-9 z^4 a^4+7 z^2 a^4-2 a^4+4 z^9 a^3-11 z^7 a^3+16 z^5 a^3-9 z^3 a^3+2 z a^3+4 z^8 a^2-7 z^6 a^2+2 z^4 a^2+3 z^2 a^2-a^2+4 z^7 a-8 z^5 a+3 z^3 a+3 z^6-7 z^4+3 z^2+z^5 a^{-1} -2 z^3 a^{-1} }[/math] |
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