K12a1176
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+10 q-13+17 q^{-1} -18 q^{-2} +17 q^{-3} -14 q^{-4} +10 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+9 t^3-15 t^2+20 t-21+20 t^{-1} -15 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+12 z^6+9 z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+24 a^2 z^6-6 z^6-12 a^4 z^4+33 a^2 z^4-12 z^4-9 a^4 z^2+20 a^2 z^2-9 z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+4 a^4 z^{10}+9 a^2 z^{10}+5 z^{10}+4 a^5 z^9-2 a^3 z^9-a z^9+5 z^9 a^{-1} +4 a^6 z^8-12 a^4 z^8-40 a^2 z^8+3 z^8 a^{-2} -21 z^8+4 a^7 z^7-6 a^5 z^7-8 a^3 z^7-20 a z^7-21 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-3 a^6 z^6+22 a^4 z^6+69 a^2 z^6-12 z^6 a^{-2} +29 z^6+a^9 z^5-5 a^7 z^5+6 a^5 z^5+21 a^3 z^5+38 a z^5+25 z^5 a^{-1} -4 z^5 a^{-3} -6 a^8 z^4-3 a^6 z^4-20 a^4 z^4-56 a^2 z^4+11 z^4 a^{-2} -22 z^4-2 a^9 z^3-a^7 z^3-5 a^5 z^3-13 a^3 z^3-23 a z^3-13 z^3 a^{-1} +3 z^3 a^{-3} +3 a^8 z^2+a^6 z^2+10 a^4 z^2+24 a^2 z^2-3 z^2 a^{-2} +9 z^2+a^9 z+a^7 z+a^5 z+3 a^3 z+4 a z+2 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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