K12a716
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+2 q^{-1} -2 q^{-2} +4 q^{-3} -4 q^{-4} +5 q^{-5} -5 q^{-6} +5 q^{-7} -5 q^{-8} +4 q^{-9} -3 q^{-10} +2 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+5 t^3-5 t^2+5 t-5+5 t^{-1} -5 t^{-2} +5 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+16 z^6+15 z^4+7 z^2+1 }[/math] |
| Determinant | 43 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+9 a^6 z^8-a^4 z^8-7 a^8 z^6+30 a^6 z^6-7 a^4 z^6-16 a^8 z^4+46 a^6 z^4-15 a^4 z^4-14 a^8 z^2+31 a^6 z^2-10 a^4 z^2-4 a^8+6 a^6-a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}-z a^{15}+2 z^4 a^{14}-2 z^2 a^{14}+2 z^5 a^{13}-z^3 a^{13}+2 z^6 a^{12}-2 z^4 a^{12}+z^2 a^{12}+2 z^7 a^{11}-4 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+2 z^8 a^{10}-6 z^6 a^{10}+5 z^4 a^{10}-2 z^2 a^{10}+2 z^9 a^9-8 z^7 a^9+9 z^5 a^9-5 z^3 a^9+z a^9+2 z^{10} a^8-11 z^8 a^8+22 z^6 a^8-26 z^4 a^8+17 z^2 a^8-4 a^8+z^{11} a^7-4 z^9 a^7+12 z^5 a^7-13 z^3 a^7+4 z a^7+4 z^{10} a^6-28 z^8 a^6+68 z^6 a^6-74 z^4 a^6+37 z^2 a^6-6 a^6+z^{11} a^5-5 z^9 a^5+3 z^7 a^5+12 z^5 a^5-13 z^3 a^5+2 z a^5+2 z^{10} a^4-15 z^8 a^4+38 z^6 a^4-39 z^4 a^4+15 z^2 a^4-a^4+z^9 a^3-7 z^7 a^3+15 z^5 a^3-10 z^3 a^3+z a^3 }[/math] |
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