K12a119
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-8 q^9+15 q^8-23 q^7+27 q^6-30 q^5+28 q^4-22 q^3+17 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-40 t+49-40 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -3 z^6 a^{-6} -3 z^4 a^{-2} +12 z^4 a^{-4} -12 z^4 a^{-6} +3 z^4 a^{-8} -3 z^2 a^{-2} +16 z^2 a^{-4} -19 z^2 a^{-6} +8 z^2 a^{-8} -z^2 a^{-10} - a^{-2} +9 a^{-4} -12 a^{-6} +6 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-5} +z^{11} a^{-7} +4 z^{10} a^{-4} +8 z^{10} a^{-6} +4 z^{10} a^{-8} +6 z^9 a^{-3} +15 z^9 a^{-5} +16 z^9 a^{-7} +7 z^9 a^{-9} +4 z^8 a^{-2} +4 z^8 a^{-4} +5 z^8 a^{-6} +13 z^8 a^{-8} +8 z^8 a^{-10} +z^7 a^{-1} -14 z^7 a^{-3} -37 z^7 a^{-5} -24 z^7 a^{-7} +5 z^7 a^{-9} +7 z^7 a^{-11} -13 z^6 a^{-2} -40 z^6 a^{-4} -56 z^6 a^{-6} -36 z^6 a^{-8} -3 z^6 a^{-10} +4 z^6 a^{-12} -3 z^5 a^{-1} +3 z^5 a^{-3} +6 z^5 a^{-5} -21 z^5 a^{-7} -31 z^5 a^{-9} -9 z^5 a^{-11} +z^5 a^{-13} +15 z^4 a^{-2} +51 z^4 a^{-4} +65 z^4 a^{-6} +25 z^4 a^{-8} -10 z^4 a^{-10} -6 z^4 a^{-12} +3 z^3 a^{-1} +9 z^3 a^{-3} +26 z^3 a^{-5} +49 z^3 a^{-7} +36 z^3 a^{-9} +6 z^3 a^{-11} -z^3 a^{-13} -7 z^2 a^{-2} -29 z^2 a^{-4} -36 z^2 a^{-6} -9 z^2 a^{-8} +8 z^2 a^{-10} +3 z^2 a^{-12} -z a^{-1} -4 z a^{-3} -15 z a^{-5} -24 z a^{-7} -15 z a^{-9} -3 z a^{-11} + a^{-2} +9 a^{-4} +12 a^{-6} +6 a^{-8} + a^{-10} }[/math] |
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