K12a848
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +12 q^{-2} -17 q^{-3} +23 q^{-4} -25 q^{-5} +24 q^{-6} -21 q^{-7} +15 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+21 t^2-31 t+35-31 t^{-1} +21 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+7 z^4+4 z^2+1 }[/math] |
| Determinant | 161 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+z^8 a^6+4 z^6 a^6+4 z^4 a^6-z^2 a^6-3 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+11 z^2 a^4+5 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-12 z^5 a^{11}+5 z^3 a^{11}-z a^{11}+10 z^8 a^{10}-15 z^6 a^{10}+6 z^4 a^{10}+9 z^9 a^9-13 z^7 a^9+6 z^5 a^9+6 z^{10} a^8-8 z^8 a^8+8 z^6 a^8-9 z^4 a^8+5 z^2 a^8+2 z^{11} a^7+6 z^9 a^7-22 z^7 a^7+25 z^5 a^7-10 z^3 a^7-z a^7+10 z^{10} a^6-31 z^8 a^6+42 z^6 a^6-26 z^4 a^6+z^2 a^6+3 a^6+2 z^{11} a^5+z^9 a^5-14 z^7 a^5+16 z^5 a^5-4 z^3 a^5-3 z a^5+4 z^{10} a^4-10 z^8 a^4+3 z^6 a^4+8 z^4 a^4-11 z^2 a^4+5 a^4+4 z^9 a^3-12 z^7 a^3+6 z^5 a^3+4 z^3 a^3-2 z a^3+3 z^8 a^2-12 z^6 a^2+14 z^4 a^2-6 z^2 a^2+a^2+z^7 a-4 z^5 a+4 z^3 a-z a }[/math] |
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