K12n566
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-3 q^2+5 q-7+10 q^{-1} -10 q^{-2} +10 q^{-3} -8 q^{-4} +5 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+16 t-23+16 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-4 z^4 }[/math] |
| Determinant | 63 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6-z^4 a^4-2 z^4 a^2-2 z^2 a^2-z^4+1+z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+2 a^5 z^9+5 a^3 z^9+3 a z^9+a^6 z^8-a^4 z^8+2 a^2 z^8+4 z^8-9 a^5 z^7-21 a^3 z^7-9 a z^7+3 z^7 a^{-1} -2 a^6 z^6-5 a^4 z^6-18 a^2 z^6+z^6 a^{-2} -14 z^6+3 a^7 z^5+21 a^5 z^5+35 a^3 z^5+7 a z^5-10 z^5 a^{-1} +a^8 z^4+4 a^6 z^4+16 a^4 z^4+29 a^2 z^4-3 z^4 a^{-2} +13 z^4-6 a^7 z^3-18 a^5 z^3-22 a^3 z^3-4 a z^3+6 z^3 a^{-1} -2 a^8 z^2-3 a^6 z^2-8 a^4 z^2-14 a^2 z^2+z^2 a^{-2} -6 z^2+2 a^7 z+6 a^5 z+6 a^3 z+2 a z+1 }[/math] |
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