K12n563
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-9 q^6+11 q^5-12 q^4+11 q^3-9 q^2+6 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^2+18 t-25+18 t^{-1} -5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^4-2 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} +z^2 a^{-2} -6 z^2 a^{-4} +z^2 a^{-6} +z^2 a^{-8} +z^2+2 a^{-2} -4 a^{-4} +2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} -3 z^8 a^{-4} +z^8 a^{-6} +4 z^8 a^{-8} -2 z^7 a^{-3} -12 z^7 a^{-5} -7 z^7 a^{-7} +3 z^7 a^{-9} +4 z^6 a^{-2} +13 z^6 a^{-4} -3 z^6 a^{-6} -11 z^6 a^{-8} +z^6 a^{-10} +2 z^5 a^{-1} +8 z^5 a^{-3} +22 z^5 a^{-5} +7 z^5 a^{-7} -9 z^5 a^{-9} -6 z^4 a^{-2} -20 z^4 a^{-4} -3 z^4 a^{-6} +7 z^4 a^{-8} -3 z^4 a^{-10} +z^4-2 z^3 a^{-1} -6 z^3 a^{-3} -20 z^3 a^{-5} -10 z^3 a^{-7} +6 z^3 a^{-9} +6 z^2 a^{-2} +16 z^2 a^{-4} +4 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -2 z^2+2 z a^{-3} +6 z a^{-5} +4 z a^{-7} -2 a^{-2} -4 a^{-4} -2 a^{-6} +1 }[/math] |
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