K12a720
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +9 q^{-2} -12 q^{-3} +16 q^{-4} -17 q^{-5} +16 q^{-6} -14 q^{-7} +10 q^{-8} -6 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+16 t^2-20 t+21-20 t^{-1} +16 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 113 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-4 z^2 a^8-a^8+z^8 a^6+5 z^6 a^6+8 z^4 a^6+5 z^2 a^6+z^8 a^4+5 z^6 a^4+8 z^4 a^4+6 z^2 a^4+2 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-6 z^4 a^{12}+3 z^2 a^{12}+4 z^7 a^{11}-5 z^5 a^{11}-z^3 a^{11}+z a^{11}+4 z^8 a^{10}-3 z^6 a^{10}-3 z^4 a^{10}+z^2 a^{10}+4 z^9 a^9-7 z^7 a^9+10 z^5 a^9-9 z^3 a^9+2 z a^9+3 z^{10} a^8-6 z^8 a^8+9 z^6 a^8-7 z^4 a^8+4 z^2 a^8-a^8+z^{11} a^7+4 z^9 a^7-21 z^7 a^7+34 z^5 a^7-18 z^3 a^7+2 z a^7+6 z^{10} a^6-21 z^8 a^6+26 z^6 a^6-12 z^4 a^6+3 z^2 a^6+z^{11} a^5+4 z^9 a^5-27 z^7 a^5+39 z^5 a^5-18 z^3 a^5+z a^5+3 z^{10} a^4-8 z^8 a^4-2 z^6 a^4+13 z^4 a^4-9 z^2 a^4+2 a^4+4 z^9 a^3-16 z^7 a^3+17 z^5 a^3-7 z^3 a^3+z a^3+3 z^8 a^2-13 z^6 a^2+15 z^4 a^2-6 z^2 a^2+z^7 a-4 z^5 a+3 z^3 a }[/math] |
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