K12n767
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q-3+7 q^{-1} -9 q^{-2} +12 q^{-3} -13 q^{-4} +11 q^{-5} -9 q^{-6} +6 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-9 t^2+15 t-17+15 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-5 z^4-z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8+a^6 z^6-6 a^4 z^6+a^2 z^6+4 a^6 z^4-13 a^4 z^4+4 a^2 z^4+5 a^6 z^2-12 a^4 z^2+6 a^2 z^2+2 a^6-5 a^4+4 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-3 z^4 a^{10}+2 z^2 a^{10}+3 z^7 a^9-9 z^5 a^9+6 z^3 a^9-z a^9+4 z^8 a^8-11 z^6 a^8+7 z^4 a^8-2 z^2 a^8+3 z^9 a^7-6 z^7 a^7+2 z^5 a^7-2 z^3 a^7+z a^7+z^{10} a^6+2 z^8 a^6-7 z^6 a^6+2 z^4 a^6+3 z^2 a^6-2 a^6+4 z^9 a^5-9 z^7 a^5+11 z^5 a^5-8 z^3 a^5+4 z a^5+z^{10} a^4-2 z^8 a^4+11 z^6 a^4-19 z^4 a^4+16 z^2 a^4-5 a^4+z^9 a^3+3 z^5 a^3-3 z^3 a^3+2 z a^3+6 z^6 a^2-10 z^4 a^2+8 z^2 a^2-4 a^2+3 z^5 a-3 z^3 a+z^4-z^2 }[/math] |
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