K12a734
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-19 q^6+27 q^5-33 q^4+36 q^3-33 q^2+27 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-26 t^2+46 t-55+46 t^{-1} -26 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-6 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-3 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +13 z^{10} a^{-4} +7 z^{10} a^{-6} +9 z^9 a^{-1} +17 z^9 a^{-3} +18 z^9 a^{-5} +10 z^9 a^{-7} +6 z^8 a^{-2} -10 z^8 a^{-4} +8 z^8 a^{-8} +8 z^8+4 a z^7-11 z^7 a^{-1} -35 z^7 a^{-3} -40 z^7 a^{-5} -16 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-31 z^6 a^{-2} -15 z^6 a^{-4} -17 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5-2 z^5 a^{-1} +16 z^5 a^{-3} +25 z^5 a^{-5} +7 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+27 z^4 a^{-2} +14 z^4 a^{-4} +12 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +12 z^4+5 a z^3+6 z^3 a^{-1} +2 z^3 a^{-3} -4 z^3 a^{-5} +5 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-2 z a^{-1} -z a^{-3} -z a^{-5} -2 z a^{-7} -z a^{-9} +1 }[/math] |
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