K12a619
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+5 q^9-8 q^8+11 q^7-13 q^6+14 q^5-13 q^4+11 q^3-8 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+24 t-35+24 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-6 z^4 }[/math] |
| Determinant | 95 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -2 z^4 a^{-4} -2 z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-10} +z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +4 z^9 a^{-5} +4 z^9 a^{-7} +3 z^9 a^{-9} +3 z^9 a^{-11} +4 z^8 a^{-4} -7 z^8 a^{-6} -25 z^8 a^{-8} -13 z^8 a^{-10} +z^8 a^{-12} +4 z^7 a^{-3} -9 z^7 a^{-5} -29 z^7 a^{-7} -32 z^7 a^{-9} -16 z^7 a^{-11} +3 z^6 a^{-2} -5 z^6 a^{-4} +5 z^6 a^{-6} +31 z^6 a^{-8} +13 z^6 a^{-10} -5 z^6 a^{-12} +2 z^5 a^{-1} -5 z^5 a^{-3} +10 z^5 a^{-5} +49 z^5 a^{-7} +58 z^5 a^{-9} +26 z^5 a^{-11} -2 z^4 a^{-2} +z^4 a^{-4} -5 z^4 a^{-6} -16 z^4 a^{-8} +7 z^4 a^{-12} +z^4-2 z^3 a^{-1} +4 z^3 a^{-3} -9 z^3 a^{-5} -38 z^3 a^{-7} -38 z^3 a^{-9} -15 z^3 a^{-11} +2 z^2 a^{-4} +z^2 a^{-6} +3 z^2 a^{-8} -z^2 a^{-10} -3 z^2 a^{-12} -2 z^2+3 z a^{-5} +9 z a^{-7} +9 z a^{-9} +3 z a^{-11} +1 }[/math] |
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