K12a410
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+25 q^8-31 q^7+33 q^6-31 q^5+26 q^4-17 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+22 t^2-48 t+61-48 t^{-1} +22 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-2 z^4+4 z^2+1 }[/math] |
| Determinant | 209 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-8} +z^2 a^{-10} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +13 z^{10} a^{-8} +7 z^{10} a^{-10} +9 z^9 a^{-5} +15 z^9 a^{-7} +16 z^9 a^{-9} +10 z^9 a^{-11} +8 z^8 a^{-4} +2 z^8 a^{-6} -20 z^8 a^{-8} -6 z^8 a^{-10} +8 z^8 a^{-12} +4 z^7 a^{-3} -14 z^7 a^{-5} -39 z^7 a^{-7} -48 z^7 a^{-9} -23 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -22 z^6 a^{-6} +8 z^6 a^{-8} -8 z^6 a^{-10} -19 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +5 z^5 a^{-5} +39 z^5 a^{-7} +56 z^5 a^{-9} +21 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +13 z^4 a^{-4} +19 z^4 a^{-6} +2 z^4 a^{-8} +14 z^4 a^{-10} +14 z^4 a^{-12} -2 z^4 a^{-14} +4 z^3 a^{-3} -2 z^3 a^{-5} -25 z^3 a^{-7} -31 z^3 a^{-9} -8 z^3 a^{-11} +4 z^3 a^{-13} +z^2 a^{-2} -6 z^2 a^{-4} -6 z^2 a^{-6} -z^2 a^{-8} -5 z^2 a^{-10} -3 z^2 a^{-12} +z a^{-5} +7 z a^{-7} +7 z a^{-9} +z a^{-11} +2 a^{-4} - a^{-8} }[/math] |
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