K12n209
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-15 q^9+20 q^8-23 q^7+22 q^6-19 q^5+14 q^4-7 q^3+3 q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+15 t^2-31 t+39-31 t^{-1} +15 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-6} -z^6 a^{-8} +3 z^4 a^{-4} -6 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +7 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-8} +2 z^{10} a^{-10} +6 z^9 a^{-7} +12 z^9 a^{-9} +6 z^9 a^{-11} +7 z^8 a^{-6} +13 z^8 a^{-8} +13 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-5} -4 z^7 a^{-7} -16 z^7 a^{-9} -5 z^7 a^{-11} +4 z^7 a^{-13} -13 z^6 a^{-6} -33 z^6 a^{-8} -36 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -3 z^5 a^{-7} -4 z^5 a^{-9} -10 z^5 a^{-11} -9 z^5 a^{-13} +6 z^4 a^{-4} +21 z^4 a^{-6} +27 z^4 a^{-8} +23 z^4 a^{-10} +9 z^4 a^{-12} -2 z^4 a^{-14} +z^3 a^{-5} +8 z^3 a^{-7} +9 z^3 a^{-9} +8 z^3 a^{-11} +6 z^3 a^{-13} -10 z^2 a^{-4} -16 z^2 a^{-6} -8 z^2 a^{-8} -5 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} -3 z a^{-5} -4 z a^{-7} -2 z a^{-9} -2 z a^{-11} -z a^{-13} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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