K12a1229
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-18 q^3+27 q^2-33 q+35-33 q^{-1} +27 q^{-2} -18 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-14 t^3+27 t^2-40 t+47-40 t^{-1} +27 t^{-2} -14 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-9 z^6-7 z^4-3 z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -19 z^6+9 a^2 z^4+9 z^4 a^{-2} -25 z^4+7 a^2 z^2+7 z^2 a^{-2} -17 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+8 z^{10} a^{-2} +16 z^{10}+10 a^3 z^9+11 a z^9+11 z^9 a^{-1} +10 z^9 a^{-3} +8 a^4 z^8-9 a^2 z^8-9 z^8 a^{-2} +8 z^8 a^{-4} -34 z^8+4 a^5 z^7-18 a^3 z^7-29 a z^7-29 z^7 a^{-1} -18 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-16 a^4 z^6+5 a^2 z^6+5 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} +44 z^6-8 a^5 z^5+12 a^3 z^5+25 a z^5+25 z^5 a^{-1} +12 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4-11 a^2 z^4-11 z^4 a^{-2} +10 z^4 a^{-4} -2 z^4 a^{-6} -46 z^4+4 a^5 z^3-6 a^3 z^3-13 a z^3-13 z^3 a^{-1} -6 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-2 a^4 z^2+10 a^2 z^2+10 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} +26 z^2+2 a^3 z+3 a z+3 z a^{-1} +2 z a^{-3} -3 a^2-3 a^{-2} -5 }[/math] |
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