K12n64
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+7 q^6-9 q^5+11 q^4-11 q^3+10 q^2-8 q+5-2 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} -10 z^4 a^{-2} +14 z^4 a^{-4} -5 z^4 a^{-6} +z^4-16 z^2 a^{-2} +18 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} +4 z^2-9 a^{-2} +10 a^{-4} -5 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +7 z^9 a^{-3} +5 z^9 a^{-5} +2 z^8 a^{-2} +10 z^8 a^{-4} +9 z^8 a^{-6} +z^8-10 z^7 a^{-1} -28 z^7 a^{-3} -11 z^7 a^{-5} +7 z^7 a^{-7} -28 z^6 a^{-2} -58 z^6 a^{-4} -34 z^6 a^{-6} +2 z^6 a^{-8} -6 z^6+16 z^5 a^{-1} +27 z^5 a^{-3} -11 z^5 a^{-5} -22 z^5 a^{-7} +56 z^4 a^{-2} +84 z^4 a^{-4} +41 z^4 a^{-6} +13 z^4-9 z^3 a^{-1} -3 z^3 a^{-3} +24 z^3 a^{-5} +22 z^3 a^{-7} +4 z^3 a^{-9} -40 z^2 a^{-2} -48 z^2 a^{-4} -23 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -12 z^2+z a^{-1} -2 z a^{-3} -8 z a^{-5} -7 z a^{-7} -2 z a^{-9} +9 a^{-2} +10 a^{-4} +5 a^{-6} + a^{-8} +4 }[/math] |
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