K12a743
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+5 q^5-7 q^4+10 q^3-11 q^2+11 q-10+8 q^{-1} -6 q^{-2} +4 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+20 t-27+20 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^4+a^4-z^4 a^2-z^2 a^2-2 z^4-3 z^2-1-2 z^4 a^{-2} -2 z^2 a^{-2} -z^4 a^{-4} + a^{-4} +z^2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+3 z^{10} a^{-2} +5 z^{10}+2 a^3 z^9-a z^9+z^9 a^{-1} +4 z^9 a^{-3} +a^4 z^8-9 a^2 z^8-11 z^8 a^{-2} +4 z^8 a^{-4} -25 z^8-11 a^3 z^7-13 a z^7-19 z^7 a^{-1} -13 z^7 a^{-3} +4 z^7 a^{-5} -6 a^4 z^6+9 a^2 z^6+15 z^6 a^{-2} -8 z^6 a^{-4} +4 z^6 a^{-6} +42 z^6+18 a^3 z^5+28 a z^5+36 z^5 a^{-1} +18 z^5 a^{-3} -5 z^5 a^{-5} +3 z^5 a^{-7} +11 a^4 z^4-10 z^4 a^{-2} +7 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} -34 z^4-11 a^3 z^3-20 a z^3-26 z^3 a^{-1} -11 z^3 a^{-3} +2 z^3 a^{-5} -4 z^3 a^{-7} -7 a^4 z^2-a^2 z^2+2 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +12 z^2+3 a^3 z+5 a z+5 z a^{-1} +3 z a^{-3} +a^4+ a^{-4} -1 }[/math] |
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