K12a1162
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-2 q^9+4 q^8-7 q^7+9 q^6-10 q^5+10 q^4-9 q^3+7 q^2-5 q+3- q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+11 t^2-13 t+13-13 t^{-1} +11 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-13 z^4-5 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} -8 z^4 a^{-4} -3 z^4 a^{-6} +z^4 a^{-8} +z^4-4 z^2 a^{-2} -7 z^2 a^{-4} -z^2 a^{-6} +3 z^2 a^{-8} +4 z^2-2 a^{-2} - a^{-4} + a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10} a^{-6} +z^9 a^{-1} -6 z^9 a^{-3} -4 z^9 a^{-5} +3 z^9 a^{-7} -4 z^8 a^{-2} -16 z^8 a^{-4} -7 z^8 a^{-6} +4 z^8 a^{-8} +z^8-5 z^7 a^{-1} +18 z^7 a^{-3} +10 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} +2 z^6 a^{-2} +36 z^6 a^{-4} +12 z^6 a^{-6} -12 z^6 a^{-8} +3 z^6 a^{-10} -7 z^6+6 z^5 a^{-1} -33 z^5 a^{-3} -15 z^5 a^{-5} +12 z^5 a^{-7} -10 z^5 a^{-9} +2 z^5 a^{-11} +6 z^4 a^{-2} -43 z^4 a^{-4} -10 z^4 a^{-6} +17 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +16 z^4+z^3 a^{-1} +26 z^3 a^{-3} +5 z^3 a^{-5} -5 z^3 a^{-7} +12 z^3 a^{-9} -3 z^3 a^{-11} -6 z^2 a^{-2} +18 z^2 a^{-4} -6 z^2 a^{-8} +3 z^2 a^{-10} -2 z^2 a^{-12} -13 z^2-2 z a^{-1} -5 z a^{-3} -z a^{-5} -2 z a^{-9} +2 a^{-2} - a^{-4} + a^{-8} +3 }[/math] |
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