K12a204
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+15 q^2-21 q+25-27 q^{-1} +25 q^{-2} -20 q^{-3} +14 q^{-4} -8 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-41 t+59-41 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4-3 z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4+2 z^2 a^4+a^4-z^6 a^2-z^4 a^2-2 z^2 a^2-z^6-z^4-3 z^2-2+2 z^4 a^{-2} +2 z^2 a^{-2} +2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+6 a^5 z^9+13 a^3 z^9+14 a z^9+7 z^9 a^{-1} +4 a^6 z^8-2 a^4 z^8-7 a^2 z^8+8 z^8 a^{-2} +7 z^8+a^7 z^7-19 a^5 z^7-45 a^3 z^7-33 a z^7-z^7 a^{-1} +7 z^7 a^{-3} -14 a^6 z^6-23 a^4 z^6-20 a^2 z^6-5 z^6 a^{-2} +4 z^6 a^{-4} -20 z^6-3 a^7 z^5+17 a^5 z^5+46 a^3 z^5+24 a z^5-12 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+32 a^4 z^4+27 a^2 z^4-8 z^4 a^{-2} -6 z^4 a^{-4} +7 z^4+2 a^7 z^3-5 a^5 z^3-20 a^3 z^3-8 a z^3+10 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-13 a^4 z^2-10 a^2 z^2+9 z^2 a^{-2} +3 z^2 a^{-4} +5 z^2+a^5 z+4 a^3 z+a z-3 z a^{-1} -z a^{-3} +a^4-2 a^{-2} -2 }[/math] |
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