K12a210
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+10 q^{10}-17 q^9+23 q^8-29 q^7+30 q^6-27 q^5+22 q^4-14 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-43 t+55-43 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -4 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} + a^{-2} + a^{-4} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +8 z^{10} a^{-8} +5 z^{10} a^{-10} +5 z^9 a^{-5} +12 z^9 a^{-7} +16 z^9 a^{-9} +9 z^9 a^{-11} +5 z^8 a^{-4} +9 z^8 a^{-6} -z^8 a^{-8} +3 z^8 a^{-10} +8 z^8 a^{-12} +3 z^7 a^{-3} -2 z^7 a^{-5} -18 z^7 a^{-7} -34 z^7 a^{-9} -17 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -9 z^6 a^{-4} -27 z^6 a^{-6} -17 z^6 a^{-8} -18 z^6 a^{-10} -17 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -11 z^5 a^{-5} +25 z^5 a^{-9} +13 z^5 a^{-11} -8 z^5 a^{-13} -3 z^4 a^{-2} +5 z^4 a^{-4} +22 z^4 a^{-6} +11 z^4 a^{-8} +10 z^4 a^{-10} +11 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} +13 z^3 a^{-5} +9 z^3 a^{-7} -13 z^3 a^{-9} -10 z^3 a^{-11} +4 z^3 a^{-13} +3 z^2 a^{-2} -2 z^2 a^{-4} -6 z^2 a^{-6} +2 z^2 a^{-8} -z^2 a^{-10} -3 z^2 a^{-12} +z^2 a^{-14} -z a^{-3} -5 z a^{-5} -2 z a^{-7} +6 z a^{-9} +4 z a^{-11} - a^{-2} + a^{-4} -2 a^{-8} - a^{-10} }[/math] |
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