K12n623
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^7+4 q^6-6 q^5+8 q^4-8 q^3+9 q^2-7 q+5-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-8 t+5-8 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+3 z^2+1 }[/math] |
| Determinant | 53 |
| 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^4-10 z^2 a^{-2} +15 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +3 z^2-3 a^{-2} +6 a^{-4} -3 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +8 z^9 a^{-3} +5 z^9 a^{-5} -6 z^8 a^{-2} -2 z^8 a^{-4} +5 z^8 a^{-6} +z^8-16 z^7 a^{-1} -39 z^7 a^{-3} -21 z^7 a^{-5} +2 z^7 a^{-7} -6 z^6 a^{-2} -23 z^6 a^{-4} -22 z^6 a^{-6} -5 z^6+26 z^5 a^{-1} +53 z^5 a^{-3} +20 z^5 a^{-5} -7 z^5 a^{-7} +24 z^4 a^{-2} +42 z^4 a^{-4} +27 z^4 a^{-6} +z^4 a^{-8} +8 z^4-14 z^3 a^{-1} -22 z^3 a^{-3} -2 z^3 a^{-5} +6 z^3 a^{-7} -16 z^2 a^{-2} -24 z^2 a^{-4} -14 z^2 a^{-6} -z^2 a^{-8} -5 z^2+z a^{-1} +z a^{-3} -3 z a^{-5} -2 z a^{-7} +z a^{-9} +3 a^{-2} +6 a^{-4} +3 a^{-6} +1 }[/math] |
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