K12n233
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-1} +2 q^{-2} -2 q^{-3} +4 q^{-4} -4 q^{-5} +5 q^{-6} -4 q^{-7} +3 q^{-8} -2 q^{-9} + q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-2 t^3+4 t^2-5 t+5-5 t^{-1} +4 t^{-2} -2 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+6 z^6+12 z^4+9 z^2+1 }[/math] |
| Determinant | 29 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-6 z^4 a^8-11 z^2 a^8-6 a^8+z^8 a^6+8 z^6 a^6+23 z^4 a^6+27 z^2 a^6+10 a^6-z^6 a^4-5 z^4 a^4-7 z^2 a^4-3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-4 z^3 a^{13}+3 z a^{13}+z^6 a^{12}-3 z^4 a^{12}+z^2 a^{12}+z^7 a^{11}-3 z^5 a^{11}+2 z^3 a^{11}-z a^{11}+z^8 a^{10}-4 z^6 a^{10}+6 z^4 a^{10}-3 z^2 a^{10}+z^9 a^9-5 z^7 a^9+9 z^5 a^9-4 z^3 a^9+z a^9+z^{10} a^8-7 z^8 a^8+20 z^6 a^8-27 z^4 a^8+22 z^2 a^8-6 a^8+2 z^9 a^7-13 z^7 a^7+32 z^5 a^7-31 z^3 a^7+11 z a^7+z^{10} a^6-8 z^8 a^6+27 z^6 a^6-44 z^4 a^6+34 z^2 a^6-10 a^6+z^9 a^5-7 z^7 a^5+20 z^5 a^5-25 z^3 a^5+9 z a^5+2 z^6 a^4-8 z^4 a^4+8 z^2 a^4-3 a^4+z^5 a^3-4 z^3 a^3+3 z a^3 }[/math] |
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