K12n509
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-6 q^5+7 q^4-8 q^3+7 q^2-6 q+5-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+8 t^2-7 t+7-7 t^{-1} +8 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-2 z^4-4 z^2+1 }[/math] |
| Determinant | 49 |
| 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} -10 z^4 a^{-2} +12 z^4 a^{-4} -5 z^4 a^{-6} +z^4-14 z^2 a^{-2} +11 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +4 z^2-6 a^{-2} +4 a^{-4} -2 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} +2 z^8 a^{-4} +3 z^8 a^{-6} +z^8-10 z^7 a^{-1} -21 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} -19 z^6 a^{-2} -23 z^6 a^{-4} -10 z^6 a^{-6} -6 z^6+14 z^5 a^{-1} +18 z^5 a^{-3} +5 z^5 a^{-5} +z^5 a^{-7} +39 z^4 a^{-2} +32 z^4 a^{-4} +10 z^4 a^{-6} +4 z^4 a^{-8} +13 z^4-4 z^3 a^{-1} +6 z^3 a^{-3} +2 z^3 a^{-5} -6 z^3 a^{-7} +2 z^3 a^{-9} -25 z^2 a^{-2} -15 z^2 a^{-4} -8 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -12 z^2-2 z a^{-1} -6 z a^{-3} -2 z a^{-5} +2 z a^{-7} +6 a^{-2} +4 a^{-4} +2 a^{-6} + a^{-8} +4 }[/math] |
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