K12a719
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+15 q^{-1} -19 q^{-2} +23 q^{-3} -23 q^{-4} +20 q^{-5} -15 q^{-6} +10 q^{-7} -5 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+33 t-41+33 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-2 a^8+z^6 a^6+3 z^4 a^6+4 z^2 a^6+2 a^6+2 z^6 a^4+6 z^4 a^4+6 z^2 a^4+a^4+z^6 a^2+z^4 a^2-z^2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+2 z^8 a^{10}-8 z^6 a^{10}+10 z^4 a^{10}-4 z^2 a^{10}+2 z^9 a^9-3 z^7 a^9-7 z^5 a^9+13 z^3 a^9-4 z a^9+2 z^{10} a^8-3 z^8 a^8+2 z^6 a^8-9 z^4 a^8+9 z^2 a^8-2 a^8+z^{11} a^7+2 z^9 a^7-4 z^7 a^7-4 z^5 a^7+4 z^3 a^7+6 z^{10} a^6-14 z^8 a^6+23 z^6 a^6-29 z^4 a^6+14 z^2 a^6-2 a^6+z^{11} a^5+8 z^9 a^5-19 z^7 a^5+18 z^5 a^5-9 z^3 a^5+z a^5+4 z^{10} a^4+z^8 a^4-8 z^6 a^4+6 z^4 a^4-3 z^2 a^4+a^4+8 z^9 a^3-11 z^7 a^3+7 z^5 a^3-3 z^3 a^3+z a^3+10 z^8 a^2-17 z^6 a^2+11 z^4 a^2-3 z^2 a^2+8 z^7 a-12 z^5 a+4 z^3 a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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