K12n762
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-9 q^5+10 q^4-11 q^3+11 q^2-8 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-12 t+13-12 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -9 z^4 a^{-2} +13 z^4 a^{-4} -5 z^4 a^{-6} +z^4-11 z^2 a^{-2} +13 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +3 z^2-3 a^{-2} +4 a^{-4} -3 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} -4 z^8 a^{-2} +2 z^8 a^{-4} +7 z^8 a^{-6} +z^8-15 z^7 a^{-1} -40 z^7 a^{-3} -21 z^7 a^{-5} +4 z^7 a^{-7} -14 z^6 a^{-2} -35 z^6 a^{-4} -25 z^6 a^{-6} +z^6 a^{-8} -5 z^6+23 z^5 a^{-1} +50 z^5 a^{-3} +18 z^5 a^{-5} -9 z^5 a^{-7} +36 z^4 a^{-2} +52 z^4 a^{-4} +27 z^4 a^{-6} +2 z^4 a^{-8} +9 z^4-11 z^3 a^{-1} -20 z^3 a^{-3} -8 z^3 a^{-5} +4 z^3 a^{-7} +3 z^3 a^{-9} -22 z^2 a^{-2} -26 z^2 a^{-4} -15 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -7 z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} -z a^{-9} +3 a^{-2} +4 a^{-4} +3 a^{-6} + a^{-8} +2 }[/math] |
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