K12a489
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-18 q^6+26 q^5-32 q^4+34 q^3-31 q^2+25 q-17+9 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-20 t^2+50 t-65+50 t^{-1} -20 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-2 z^4-3 z^2+1 }[/math] |
| Determinant | 211 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -2 z^4 a^{-2} +5 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-7 z^2 a^{-2} +8 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} -z^2+a^2-4 a^{-2} +5 a^{-4} -3 a^{-6} + a^{-8} +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} +8 z^9 a^{-1} +16 z^9 a^{-3} +18 z^9 a^{-5} +10 z^9 a^{-7} -15 z^8 a^{-4} -z^8 a^{-6} +8 z^8 a^{-8} +6 z^8+3 a z^7-14 z^7 a^{-1} -46 z^7 a^{-3} -51 z^7 a^{-5} -18 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-20 z^6 a^{-2} -15 z^6 a^{-4} -24 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -11 z^6-6 a z^5+13 z^5 a^{-1} +51 z^5 a^{-3} +49 z^5 a^{-5} +9 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+29 z^4 a^{-2} +38 z^4 a^{-4} +31 z^4 a^{-6} +10 z^4 a^{-8} -2 z^4 a^{-10} +7 z^4+3 a z^3-12 z^3 a^{-1} -27 z^3 a^{-3} -18 z^3 a^{-5} -2 z^3 a^{-7} +4 z^3 a^{-9} +3 a^2 z^2-20 z^2 a^{-2} -23 z^2 a^{-4} -15 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -3 z^2+3 z a^{-1} +5 z a^{-3} +3 z a^{-5} -z a^{-9} -a^2+4 a^{-2} +5 a^{-4} +3 a^{-6} + a^{-8} +1 }[/math] |
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