K12n157
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+3 q^9-6 q^8+9 q^7-11 q^6+12 q^5-12 q^4+10 q^3-6 q^2+4 q-1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-6 t^2+18 t-25+18 t^{-1} -6 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+3 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-4} -z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -z^2 a^{-2} +8 z^2 a^{-4} -7 z^2 a^{-6} +3 z^2 a^{-8} +4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +3 z^9 a^{-5} +6 z^9 a^{-7} +3 z^9 a^{-9} +3 z^8 a^{-4} +5 z^8 a^{-6} +5 z^8 a^{-8} +3 z^8 a^{-10} +z^7 a^{-3} -7 z^7 a^{-5} -17 z^7 a^{-7} -8 z^7 a^{-9} +z^7 a^{-11} -8 z^6 a^{-4} -25 z^6 a^{-6} -29 z^6 a^{-8} -12 z^6 a^{-10} +2 z^5 a^{-3} +8 z^5 a^{-5} +9 z^5 a^{-7} -z^5 a^{-9} -4 z^5 a^{-11} +4 z^4 a^{-2} +17 z^4 a^{-4} +33 z^4 a^{-6} +34 z^4 a^{-8} +14 z^4 a^{-10} +z^3 a^{-1} -z^3 a^{-3} -5 z^3 a^{-5} +8 z^3 a^{-9} +5 z^3 a^{-11} -3 z^2 a^{-2} -15 z^2 a^{-4} -21 z^2 a^{-6} -15 z^2 a^{-8} -6 z^2 a^{-10} +z a^{-3} +z a^{-5} -2 z a^{-9} -2 z a^{-11} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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