K12a981
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+11 q-15+20 q^{-1} -20 q^{-2} +20 q^{-3} -16 q^{-4} +11 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-17 t^2+23 t-25+23 t^{-1} -17 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+13 z^4+6 z^2+1 }[/math] |
| Determinant | 135 |
| 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+39 a^2 z^4-13 z^4-13 a^4 z^2+32 a^2 z^2-13 z^2-6 a^4+12 a^2-5 }[/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}+6 a^5 z^9+2 a^3 z^9+a z^9+5 z^9 a^{-1} +6 a^6 z^8-13 a^4 z^8-41 a^2 z^8+3 z^8 a^{-2} -19 z^8+5 a^7 z^7-12 a^5 z^7-22 a^3 z^7-25 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-10 a^6 z^6+20 a^4 z^6+71 a^2 z^6-11 z^6 a^{-2} +27 z^6+a^9 z^5-8 a^7 z^5+11 a^5 z^5+43 a^3 z^5+48 a z^5+21 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+6 a^6 z^4-19 a^4 z^4-66 a^2 z^4+9 z^4 a^{-2} -27 z^4-2 a^9 z^3+3 a^7 z^3-3 a^5 z^3-33 a^3 z^3-41 a z^3-12 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-2 a^6 z^2+17 a^4 z^2+37 a^2 z^2-z^2 a^{-2} +16 z^2+a^9 z-2 a^7 z+a^5 z+12 a^3 z+13 a z+4 z a^{-1} -z a^{-3} -6 a^4-12 a^2-5 }[/math] |
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