K12a305
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+15 q^5-21 q^4+25 q^3-26 q^2+24 q-18+13 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+35 t-41+35 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-11 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-12 z^2 a^{-2} +8 z^2 a^{-4} -2 z^2 a^{-6} +11 z^2-2 a^2-5 a^{-2} +3 a^{-4} - a^{-6} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10}+4 a z^9+10 z^9 a^{-1} +16 z^9 a^{-3} +10 z^9 a^{-5} +3 a^2 z^8-10 z^8 a^{-2} +4 z^8 a^{-4} +11 z^8 a^{-6} +a^3 z^7-10 a z^7-35 z^7 a^{-1} -50 z^7 a^{-3} -18 z^7 a^{-5} +8 z^7 a^{-7} -11 a^2 z^6-18 z^6 a^{-2} -32 z^6 a^{-4} -21 z^6 a^{-6} +4 z^6 a^{-8} -22 z^6-4 a^3 z^5+2 a z^5+34 z^5 a^{-1} +55 z^5 a^{-3} +14 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+39 z^4 a^{-2} +43 z^4 a^{-4} +17 z^4 a^{-6} -5 z^4 a^{-8} +31 z^4+5 a^3 z^3+6 a z^3-13 z^3 a^{-1} -22 z^3 a^{-3} -3 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} -7 a^2 z^2-25 z^2 a^{-2} -19 z^2 a^{-4} -7 z^2 a^{-6} -20 z^2-2 a^3 z-3 a z+2 z a^{-3} -z a^{-7} +2 a^2+5 a^{-2} +3 a^{-4} + a^{-6} +6 }[/math] |
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