K12n471
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-6 q^6+9 q^5-11 q^4+12 q^3-11 q^2+9 q-5+3 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+16 t-19+16 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+2 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +3 z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -z^4+3 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2+ a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +4 z^9 a^{-3} +3 z^9 a^{-5} -4 z^8 a^{-2} +z^8 a^{-4} +5 z^8 a^{-6} -4 z^7 a^{-1} -15 z^7 a^{-3} -6 z^7 a^{-5} +5 z^7 a^{-7} +13 z^6 a^{-2} -6 z^6 a^{-4} -13 z^6 a^{-6} +3 z^6 a^{-8} +3 z^6+a z^5+13 z^5 a^{-1} +31 z^5 a^{-3} +6 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} -15 z^4 a^{-2} +13 z^4 a^{-4} +14 z^4 a^{-6} -6 z^4 a^{-8} -8 z^4-3 a z^3-18 z^3 a^{-1} -25 z^3 a^{-3} +8 z^3 a^{-7} -2 z^3 a^{-9} +5 z^2 a^{-2} -7 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +5 z^2+2 a z+6 z a^{-1} +6 z a^{-3} -2 z a^{-7} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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