K12a672
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-21 q^6+30 q^5-37 q^4+39 q^3-35 q^2+29 q-19+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-29 t^2+50 t-59+50 t^{-1} -29 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 243 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-7 z^4 a^{-2} -z^4 a^{-4} +2 z^4 a^{-6} +3 z^4-6 z^2 a^{-2} +4 z^2 a^{-4} +3 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +8 z^{10} a^{-2} +18 z^{10} a^{-4} +10 z^{10} a^{-6} +10 z^9 a^{-1} +17 z^9 a^{-3} +21 z^9 a^{-5} +14 z^9 a^{-7} -2 z^8 a^{-2} -27 z^8 a^{-4} -6 z^8 a^{-6} +11 z^8 a^{-8} +8 z^8+4 a z^7-14 z^7 a^{-1} -44 z^7 a^{-3} -57 z^7 a^{-5} -26 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-18 z^6 a^{-2} +3 z^6 a^{-4} -17 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -15 z^6-8 a z^5+2 z^5 a^{-1} +33 z^5 a^{-3} +44 z^5 a^{-5} +13 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+21 z^4 a^{-2} +14 z^4 a^{-4} +16 z^4 a^{-6} +10 z^4 a^{-8} -z^4 a^{-10} +10 z^4+5 a z^3+4 z^3 a^{-1} -6 z^3 a^{-3} -8 z^3 a^{-5} -z^3 a^{-7} +2 z^3 a^{-9} +a^2 z^2-11 z^2 a^{-2} -9 z^2 a^{-4} -4 z^2 a^{-6} -z^2 a^{-8} -4 z^2-a z-2 z a^{-1} -z a^{-3} -z a^{-5} -z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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