K12a773
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+5 q^7-8 q^6+11 q^5-13 q^4+14 q^3-12 q^2+10 q-7+4 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+23 t-33+23 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^{-2} -2 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-z^2 a^{-2} -z^2 a^{-4} +z^2 a^{-8} -z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +2 z^9 a^{-1} -z^9 a^{-3} +z^9 a^{-5} +4 z^9 a^{-7} -7 z^8 a^{-2} -24 z^8 a^{-4} -11 z^8 a^{-6} +4 z^8 a^{-8} +2 z^8+2 a z^7-4 z^7 a^{-1} -6 z^7 a^{-3} -17 z^7 a^{-5} -14 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6+13 z^6 a^{-2} +48 z^6 a^{-4} +16 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -4 z^6-7 a z^5-z^5 a^{-1} +20 z^5 a^{-3} +40 z^5 a^{-5} +16 z^5 a^{-7} -10 z^5 a^{-9} -4 a^2 z^4-13 z^4 a^{-2} -36 z^4 a^{-4} -10 z^4 a^{-6} +9 z^4 a^{-8} -3 z^4 a^{-10} -3 z^4+6 a z^3+4 z^3 a^{-1} -15 z^3 a^{-3} -28 z^3 a^{-5} -9 z^3 a^{-7} +6 z^3 a^{-9} +4 a^2 z^2+6 z^2 a^{-2} +10 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} +5 z^2-2 a z-2 z a^{-1} +3 z a^{-3} +5 z a^{-5} +2 z a^{-7} -a^2- a^{-2} -1 }[/math] |
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