K12a833
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+19 q^5-22 q^4+24 q^3-21 q^2+17 q-11+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-19 t^2+29 t-33+29 t^{-1} -19 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-5 z^4+2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-9 z^4 a^{-2} -3 z^4 a^{-4} +3 z^4 a^{-6} +4 z^4-7 z^2 a^{-2} +4 z^2 a^{-4} +z^2 a^{-6} +4 z^2-2 a^{-2} +4 a^{-4} -2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +10 z^{10} a^{-4} +5 z^{10} a^{-6} +6 z^9 a^{-1} +3 z^9 a^{-3} +3 z^9 a^{-5} +6 z^9 a^{-7} -13 z^8 a^{-2} -34 z^8 a^{-4} -10 z^8 a^{-6} +6 z^8 a^{-8} +5 z^8+3 a z^7-18 z^7 a^{-1} -25 z^7 a^{-3} -17 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+9 z^6 a^{-2} +51 z^6 a^{-4} +13 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -15 z^6-9 a z^5+17 z^5 a^{-1} +45 z^5 a^{-3} +26 z^5 a^{-5} -3 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4+9 z^4 a^{-2} -25 z^4 a^{-4} -15 z^4 a^{-6} +2 z^4 a^{-8} -2 z^4 a^{-10} +12 z^4+5 a z^3-4 z^3 a^{-1} -20 z^3 a^{-3} -13 z^3 a^{-5} +4 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-8 z^2 a^{-2} -z^2 a^{-4} +2 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} -5 z^2-a z-z a^{-1} +z a^{-3} -z a^{-5} -2 z a^{-7} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1 }[/math] |
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