K12a1168
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+13 q-18+23 q^{-1} -24 q^{-2} +23 q^{-3} -19 q^{-4} +13 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-19 t^2+28 t-31+28 t^{-1} -19 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+11 z^4+3 z^2+1 }[/math] |
| Determinant | 155 |
| 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+25 a^2 z^6-6 z^6-13 a^4 z^4+37 a^2 z^4-13 z^4-11 a^4 z^2+25 a^2 z^2-11 z^2-3 a^4+6 a^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+10 a^2 z^{10}+5 z^{10}+7 a^5 z^9+4 a^3 z^9+2 a z^9+5 z^9 a^{-1} +7 a^6 z^8-6 a^4 z^8-33 a^2 z^8+3 z^8 a^{-2} -17 z^8+5 a^7 z^7-11 a^5 z^7-15 a^3 z^7-18 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-11 a^6 z^6+5 a^4 z^6+57 a^2 z^6-11 z^6 a^{-2} +27 z^6+a^9 z^5-6 a^7 z^5+9 a^5 z^5+17 a^3 z^5+27 a z^5+22 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+9 a^6 z^4-7 a^4 z^4-63 a^2 z^4+11 z^4 a^{-2} -31 z^4-2 a^9 z^3+a^7 z^3-a^5 z^3-11 a^3 z^3-24 a z^3-13 z^3 a^{-1} +4 z^3 a^{-3} +2 a^8 z^2-3 a^6 z^2+10 a^4 z^2+32 a^2 z^2-2 z^2 a^{-2} +15 z^2+a^9 z+4 a^3 z+6 a z+3 z a^{-1} -3 a^4-6 a^2-2 }[/math] |
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