K12a554
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-15 q^3+24 q^2-27 q+30-29 q^{-1} +22 q^{-2} -16 q^{-3} +9 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-45 t+65-45 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4-3 z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4+3 z^4 a^2-3 a^2-z^6+z^4+3 z^2+3-z^6 a^{-2} -2 z^4 a^{-2} -4 z^2 a^{-2} +z^4 a^{-4} +z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+7 a^3 z^9+16 a z^9+16 z^9 a^{-1} +7 z^9 a^{-3} +6 a^4 z^8+8 a^2 z^8+9 z^8 a^{-2} +7 z^8 a^{-4} +4 z^8+3 a^5 z^7-11 a^3 z^7-39 a z^7-38 z^7 a^{-1} -9 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-12 a^4 z^6-36 a^2 z^6-44 z^6 a^{-2} -17 z^6 a^{-4} +z^6 a^{-6} -49 z^6-6 a^5 z^5+9 a^3 z^5+43 a z^5+33 z^5 a^{-1} -5 z^5 a^{-3} -10 z^5 a^{-5} -3 a^6 z^4+9 a^4 z^4+46 a^2 z^4+59 z^4 a^{-2} +15 z^4 a^{-4} -2 z^4 a^{-6} +76 z^4+3 a^5 z^3-14 a^3 z^3-37 a z^3-17 z^3 a^{-1} +9 z^3 a^{-3} +6 z^3 a^{-5} +3 a^6 z^2-4 a^4 z^2-29 a^2 z^2-30 z^2 a^{-2} -7 z^2 a^{-4} -45 z^2+10 a^3 z+19 a z+11 z a^{-1} +2 z a^{-3} -a^6+3 a^2+3 }[/math] |
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