K12a649
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+10 q-14+18 q^{-1} -19 q^{-2} +19 q^{-3} -15 q^{-4} +11 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-17 t^2+25 t-27+25 t^{-1} -17 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+8 a^4 z^4-9 a^2 z^4-z^4 a^{-2} +8 z^4-3 a^6 z^2+9 a^4 z^2-7 a^2 z^2-3 z^2 a^{-2} +8 z^2-2 a^6+3 a^4-a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+5 a^5 z^9+6 a^3 z^9+5 a z^9+4 z^9 a^{-1} +6 a^6 z^8-15 a^2 z^8+3 z^8 a^{-2} -6 z^8+5 a^7 z^7-7 a^5 z^7-23 a^3 z^7-26 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-11 a^6 z^6-13 a^4 z^6+7 a^2 z^6-12 z^6 a^{-2} -6 z^6+a^9 z^5-8 a^7 z^5+2 a^5 z^5+29 a^3 z^5+34 a z^5+12 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+10 a^6 z^4+23 a^4 z^4+10 a^2 z^4+13 z^4 a^{-2} +15 z^4-2 a^9 z^3+3 a^7 z^3+5 a^5 z^3-12 a^3 z^3-19 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-7 a^6 z^2-12 a^4 z^2-9 a^2 z^2-5 z^2 a^{-2} -10 z^2+a^9 z-2 a^7 z-3 a^5 z+2 a^3 z+3 a z-z a^{-3} +2 a^6+3 a^4+a^2+ a^{-2} +2 }[/math] |
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