K12a419
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+24 q^5-34 q^4+42 q^3-45 q^2+41 q-33+23 q^{-1} -12 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-32 t^2+61 t-73+61 t^{-1} -32 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 279 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-4 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +4 z^4-a^2 z^2-3 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +25 z^{10} a^{-2} +15 z^{10} a^{-4} +10 z^{10}+10 a z^9+21 z^9 a^{-1} +35 z^9 a^{-3} +24 z^9 a^{-5} +5 a^2 z^8-41 z^8 a^{-2} -z^8 a^{-4} +22 z^8 a^{-6} -13 z^8+a^3 z^7-25 a z^7-76 z^7 a^{-1} -100 z^7 a^{-3} -37 z^7 a^{-5} +13 z^7 a^{-7} -13 a^2 z^6-9 z^6 a^{-2} -44 z^6 a^{-4} -32 z^6 a^{-6} +5 z^6 a^{-8} -15 z^6-2 a^3 z^5+19 a z^5+68 z^5 a^{-1} +80 z^5 a^{-3} +20 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+32 z^4 a^{-2} +39 z^4 a^{-4} +18 z^4 a^{-6} -2 z^4 a^{-8} +24 z^4+a^3 z^3-5 a z^3-24 z^3 a^{-1} -27 z^3 a^{-3} -6 z^3 a^{-5} +3 z^3 a^{-7} -2 a^2 z^2-13 z^2 a^{-2} -12 z^2 a^{-4} -4 z^2 a^{-6} -7 z^2+a z+5 z a^{-1} +5 z a^{-3} +z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
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