K12n567
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-7 q^3+12 q^2-16 q+20-19 q^{-1} +17 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+13 t^2-26 t+33-26 t^{-1} +13 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-5 z^4-z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-2 z^6+a^4 z^4-2 a^2 z^4+2 z^4 a^{-2} -6 z^4+2 a^4 z^2-2 a^2 z^2+3 z^2 a^{-2} -4 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+5 a^3 z^9+10 a z^9+5 z^9 a^{-1} +5 a^4 z^8+6 a^2 z^8+4 z^8 a^{-2} +5 z^8+3 a^5 z^7-9 a^3 z^7-21 a z^7-8 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-12 a^4 z^6-22 a^2 z^6-z^6 a^{-2} -10 z^6-8 a^5 z^5+3 a^3 z^5+19 a z^5+15 z^5 a^{-1} +7 z^5 a^{-3} -3 a^6 z^4+9 a^4 z^4+20 a^2 z^4-2 z^4 a^{-2} +3 z^4 a^{-4} +3 z^4+6 a^5 z^3+2 a^3 z^3-9 a z^3-14 z^3 a^{-1} -9 z^3 a^{-3} +2 a^6 z^2-4 a^4 z^2-8 a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +z^2-2 a^5 z-3 a^3 z+2 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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