K12a1283
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+4 q^4-7 q^3+9 q^2-11 q+13-11 q^{-1} +9 q^{-2} -7 q^{-3} +4 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-6 t^3+10 t^2-13 t+15-13 t^{-1} +10 t^{-2} -6 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-17 z^6-16 z^4-4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -9 z^8+7 a^2 z^6+7 z^6 a^{-2} -31 z^6+17 a^2 z^4+17 z^4 a^{-2} -50 z^4+16 a^2 z^2+16 z^2 a^{-2} -36 z^2+4 a^2+4 a^{-2} -7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+2 z^{10} a^{-2} +5 z^{10}+4 a^3 z^9-2 z^9 a^{-1} +2 z^9 a^{-3} +3 a^4 z^8-14 a^2 z^8-9 z^8 a^{-2} +2 z^8 a^{-4} -28 z^8+2 a^5 z^7-19 a^3 z^7-16 a z^7-3 z^7 a^{-1} -6 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-11 a^4 z^6+26 a^2 z^6+23 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +67 z^6-7 a^5 z^5+33 a^3 z^5+42 a z^5+18 z^5 a^{-1} +9 z^5 a^{-3} -7 z^5 a^{-5} -4 a^6 z^4+10 a^4 z^4-24 a^2 z^4-31 z^4 a^{-2} +2 z^4 a^{-4} -4 z^4 a^{-6} -75 z^4+4 a^5 z^3-25 a^3 z^3-31 a z^3-18 z^3 a^{-1} -10 z^3 a^{-3} +6 z^3 a^{-5} +3 a^6 z^2-4 a^4 z^2+15 a^2 z^2+18 z^2 a^{-2} -z^2 a^{-4} +4 z^2 a^{-6} +45 z^2+4 a^3 z+7 a z+5 z a^{-1} +z a^{-3} -z a^{-5} -4 a^2-4 a^{-2} -7 }[/math] |
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