K12n445
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^{10}-7 q^9+12 q^8-18 q^7+21 q^6-21 q^5+20 q^4-14 q^3+9 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-30 t+39-30 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 129 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-8} +z^2 a^{-2} +z^2 a^{-4} +4 z^2 a^{-6} -2 z^2 a^{-8} + a^{-4} +3 a^{-6} -4 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-6} +2 z^{10} a^{-8} +6 z^9 a^{-5} +11 z^9 a^{-7} +5 z^9 a^{-9} +7 z^8 a^{-4} +11 z^8 a^{-6} +8 z^8 a^{-8} +4 z^8 a^{-10} +4 z^7 a^{-3} -7 z^7 a^{-5} -18 z^7 a^{-7} -6 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-2} -16 z^6 a^{-4} -32 z^6 a^{-6} -16 z^6 a^{-8} -z^6 a^{-10} -9 z^5 a^{-3} -5 z^5 a^{-5} +12 z^5 a^{-7} +15 z^5 a^{-9} +7 z^5 a^{-11} -2 z^4 a^{-2} +11 z^4 a^{-4} +21 z^4 a^{-6} +7 z^4 a^{-8} +2 z^4 a^{-10} +3 z^4 a^{-12} +5 z^3 a^{-3} +3 z^3 a^{-5} -15 z^3 a^{-7} -22 z^3 a^{-9} -9 z^3 a^{-11} +z^2 a^{-2} -4 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2 a^{-8} -2 z^2 a^{-10} -2 z^2 a^{-12} +z a^{-5} +9 z a^{-7} +11 z a^{-9} +3 z a^{-11} + a^{-4} -3 a^{-6} -4 a^{-8} - a^{-10} }[/math] |
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