K12a705
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-25 q^3+38 q^2-46 q+50-47 q^{-1} +38 q^{-2} -26 q^{-3} +14 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+33 t^2-68 t+87-68 t^{-1} +33 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-z^4-z^2+1 }[/math] |
| Determinant | 309 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +5 z^4+a^4 z^2-4 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +4 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +14 a^2 z^{10}+13 z^{10} a^{-2} +27 z^{10}+19 a^3 z^9+39 a z^9+37 z^9 a^{-1} +17 z^9 a^{-3} +13 a^4 z^8+2 z^8 a^{-2} +12 z^8 a^{-4} -23 z^8+5 a^5 z^7-33 a^3 z^7-100 a z^7-93 z^7 a^{-1} -26 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-44 a^2 z^6-44 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -44 z^6-6 a^5 z^5+23 a^3 z^5+78 a z^5+69 z^5 a^{-1} +13 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+16 a^4 z^4+43 a^2 z^4+42 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +53 z^4+2 a^5 z^3-10 a^3 z^3-30 a z^3-23 z^3 a^{-1} -2 z^3 a^{-3} +3 z^3 a^{-5} -6 a^4 z^2-16 a^2 z^2-13 z^2 a^{-2} -4 z^2 a^{-4} -19 z^2+3 a^3 z+6 a z+4 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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