K12a476
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-4 q+9-14 q^{-1} +20 q^{-2} -23 q^{-3} +25 q^{-4} -23 q^{-5} +18 q^{-6} -13 q^{-7} +7 q^{-8} -3 q^{-9} + q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-33 t+39-33 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4+1 }[/math] |
| Determinant | 161 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^8+3 z^2 a^8+2 a^8-2 z^6 a^6-8 z^4 a^6-11 z^2 a^6-6 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+13 z^2 a^4+6 a^4-2 z^6 a^2-7 z^4 a^2-7 z^2 a^2-2 a^2+z^4+2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-2 z^3 a^{11}+6 z^6 a^{10}-5 z^4 a^{10}+2 z^2 a^{10}+10 z^7 a^9-16 z^5 a^9+14 z^3 a^9-4 z a^9+12 z^8 a^8-22 z^6 a^8+15 z^4 a^8-5 z^2 a^8+2 a^8+11 z^9 a^7-19 z^7 a^7+11 z^3 a^7-6 z a^7+7 z^{10} a^6-5 z^8 a^6-29 z^6 a^6+39 z^4 a^6-23 z^2 a^6+6 a^6+2 z^{11} a^5+14 z^9 a^5-64 z^7 a^5+70 z^5 a^5-29 z^3 a^5+2 z a^5+12 z^{10} a^4-34 z^8 a^4+8 z^6 a^4+31 z^4 a^4-24 z^2 a^4+6 a^4+2 z^{11} a^3+7 z^9 a^3-52 z^7 a^3+74 z^5 a^3-35 z^3 a^3+6 z a^3+5 z^{10} a^2-16 z^8 a^2+5 z^6 a^2+19 z^4 a^2-13 z^2 a^2+2 a^2+4 z^9 a-17 z^7 a+23 z^5 a-11 z^3 a+2 z a+z^8-4 z^6+6 z^4-4 z^2+1 }[/math] |
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