K12n326
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+6 q^6-8 q^5+9 q^4-8 q^3+8 q^2-5 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+8 t^2-9 t+9-9 t^{-1} +8 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 53 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +13 z^4 a^{-4} -5 z^4 a^{-6} -4 z^2 a^{-2} +14 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} - a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +5 z^9 a^{-5} +2 z^9 a^{-7} +3 z^8 a^{-2} +3 z^8 a^{-4} +z^8 a^{-6} +z^8 a^{-8} +z^7 a^{-1} -10 z^7 a^{-3} -18 z^7 a^{-5} -7 z^7 a^{-7} -13 z^6 a^{-2} -27 z^6 a^{-4} -18 z^6 a^{-6} -4 z^6 a^{-8} -4 z^5 a^{-1} +3 z^5 a^{-3} +11 z^5 a^{-5} +4 z^5 a^{-7} +16 z^4 a^{-2} +39 z^4 a^{-4} +30 z^4 a^{-6} +7 z^4 a^{-8} +4 z^3 a^{-1} +6 z^3 a^{-3} +8 z^3 a^{-5} +8 z^3 a^{-7} +2 z^3 a^{-9} -8 z^2 a^{-2} -23 z^2 a^{-4} -18 z^2 a^{-6} -3 z^2 a^{-8} -z a^{-1} -3 z a^{-3} -7 z a^{-5} -6 z a^{-7} -z a^{-9} + a^{-2} +6 a^{-4} +5 a^{-6} + a^{-8} }[/math] |
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