K12a98
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+16 q^5-23 q^4+28 q^3-30 q^2+28 q-22+16 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+41 t-49+41 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+1 }[/math] |
| Determinant | 191 |
| 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^4-12 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +7 z^4-2 a^2 z^2-14 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} +9 z^2-a^2-6 a^{-2} +4 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+6 a z^9+15 z^9 a^{-1} +17 z^9 a^{-3} +8 z^9 a^{-5} +4 a^2 z^8+5 z^8 a^{-2} +16 z^8 a^{-4} +10 z^8 a^{-6} +3 z^8+a^3 z^7-15 a z^7-40 z^7 a^{-1} -30 z^7 a^{-3} +2 z^7 a^{-5} +8 z^7 a^{-7} -13 a^2 z^6-56 z^6 a^{-2} -47 z^6 a^{-4} -11 z^6 a^{-6} +4 z^6 a^{-8} -37 z^6-3 a^3 z^5+6 a z^5+19 z^5 a^{-1} -z^5 a^{-3} -23 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+65 z^4 a^{-2} +41 z^4 a^{-4} +4 z^4 a^{-6} -5 z^4 a^{-8} +47 z^4+3 a^3 z^3+6 a z^3+8 z^3 a^{-1} +18 z^3 a^{-3} +21 z^3 a^{-5} +7 z^3 a^{-7} -z^3 a^{-9} -6 a^2 z^2-31 z^2 a^{-2} -18 z^2 a^{-4} -z^2 a^{-6} +2 z^2 a^{-8} -22 z^2-a^3 z-3 a z-5 z a^{-1} -7 z a^{-3} -6 z a^{-5} -2 z a^{-7} +a^2+6 a^{-2} +4 a^{-4} + a^{-6} +5 }[/math] |
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