K12a580
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+2-3 q^{-1} +6 q^{-2} -7 q^{-3} +9 q^{-4} -10 q^{-5} +10 q^{-6} -8 q^{-7} +6 q^{-8} -4 q^{-9} +2 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-6 t^3+10 t^2-11 t+11-11 t^{-1} +10 t^{-2} -6 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+10 z^6+14 z^4+7 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-5 z^4 a^8-7 z^2 a^8-3 a^8+z^8 a^6+6 z^6 a^6+12 z^4 a^6+10 z^2 a^6+3 a^6+z^8 a^4+6 z^6 a^4+12 z^4 a^4+10 z^2 a^4+2 a^4-z^6 a^2-5 z^4 a^2-6 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+2 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+2 z^7 a^{11}-3 z^5 a^{11}-z^3 a^{11}+2 z^8 a^{10}-4 z^6 a^{10}+4 z^4 a^{10}-3 z^2 a^{10}+2 z^9 a^9-6 z^7 a^9+9 z^5 a^9-4 z^3 a^9+z a^9+2 z^{10} a^8-9 z^8 a^8+19 z^6 a^8-18 z^4 a^8+13 z^2 a^8-3 a^8+z^{11} a^7-3 z^9 a^7+z^7 a^7+8 z^5 a^7-8 z^3 a^7+4 z a^7+4 z^{10} a^6-22 z^8 a^6+47 z^6 a^6-46 z^4 a^6+20 z^2 a^6-3 a^6+z^{11} a^5-3 z^9 a^5+6 z^5 a^5-7 z^3 a^5+z a^5+2 z^{10} a^4-9 z^8 a^4+12 z^6 a^4-5 z^4 a^4-5 z^2 a^4+2 a^4+2 z^9 a^3-8 z^7 a^3+6 z^5 a^3+z^3 a^3-z a^3+2 z^8 a^2-10 z^6 a^2+14 z^4 a^2-7 z^2 a^2+a^2+z^7 a-5 z^5 a+6 z^3 a-z a }[/math] |
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