K12a681
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-14 q^7+19 q^6-22 q^5+22 q^4-20 q^3+15 q^2-10 q+6-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+18 t^2-29 t+35-29 t^{-1} +18 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-4 z^4-4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -9 z^4 a^{-2} +10 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-13 z^2 a^{-2} +10 z^2 a^{-4} -7 z^2 a^{-6} +2 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^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +6 z^{10} a^{-4} +4 z^{10} a^{-6} +2 z^9 a^{-1} +3 z^9 a^{-3} +10 z^9 a^{-5} +9 z^9 a^{-7} -4 z^8 a^{-2} -11 z^8 a^{-4} +7 z^8 a^{-6} +13 z^8 a^{-8} +z^8-9 z^7 a^{-1} -18 z^7 a^{-3} -29 z^7 a^{-5} -7 z^7 a^{-7} +13 z^7 a^{-9} -10 z^6 a^{-2} -12 z^6 a^{-4} -35 z^6 a^{-6} -18 z^6 a^{-8} +9 z^6 a^{-10} -6 z^6+12 z^5 a^{-1} +13 z^5 a^{-3} +10 z^5 a^{-5} -12 z^5 a^{-7} -17 z^5 a^{-9} +4 z^5 a^{-11} +30 z^4 a^{-2} +27 z^4 a^{-4} +25 z^4 a^{-6} +6 z^4 a^{-8} -8 z^4 a^{-10} +z^4 a^{-12} +13 z^4-3 z^3 a^{-1} +10 z^3 a^{-3} +10 z^3 a^{-5} +6 z^3 a^{-7} +8 z^3 a^{-9} -z^3 a^{-11} -23 z^2 a^{-2} -13 z^2 a^{-4} -8 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2 a^{-10} -12 z^2-2 z a^{-1} -7 z a^{-3} -5 z a^{-5} -z a^{-7} -z a^{-9} +6 a^{-2} +4 a^{-4} +2 a^{-6} + a^{-8} +4 }[/math] |
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