K12a1067
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-21 q^6+32 q^5-41 q^4+44 q^3-42 q^2+35 q-24+14 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-30 t^2+61 t-75+61 t^{-1} -30 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^4-3 z^2+1 }[/math] |
| Determinant | 275 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-9 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-10 z^2 a^{-2} +8 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +3 z^2-4 a^{-2} +3 a^{-4} -2 a^{-6} + a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +13 z^{10} a^{-2} +24 z^{10} a^{-4} +11 z^{10} a^{-6} +18 z^9 a^{-1} +28 z^9 a^{-3} +23 z^9 a^{-5} +13 z^9 a^{-7} -6 z^8 a^{-2} -37 z^8 a^{-4} -9 z^8 a^{-6} +9 z^8 a^{-8} +13 z^8+5 a z^7-34 z^7 a^{-1} -79 z^7 a^{-3} -69 z^7 a^{-5} -25 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-31 z^6 a^{-2} +z^6 a^{-4} -11 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} -24 z^6-6 a z^5+21 z^5 a^{-1} +65 z^5 a^{-3} +69 z^5 a^{-5} +24 z^5 a^{-7} -7 z^5 a^{-9} -a^2 z^4+35 z^4 a^{-2} +23 z^4 a^{-4} +20 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} +16 z^4+a z^3-7 z^3 a^{-1} -20 z^3 a^{-3} -30 z^3 a^{-5} -15 z^3 a^{-7} +3 z^3 a^{-9} -17 z^2 a^{-2} -13 z^2 a^{-4} -11 z^2 a^{-6} -6 z^2 a^{-8} +z^2 a^{-10} -8 z^2+z a^{-3} +5 z a^{-5} +4 z a^{-7} +4 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} +3 }[/math] |
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