K12n837
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-8 q^3+15 q^2-22 q+28-28 q^{-1} +26 q^{-2} -20 q^{-3} +13 q^{-4} -6 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+21 t^2-35 t+41-35 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +4 z^6+a^4 z^4-4 a^2 z^4-3 z^4 a^{-2} +5 z^4+2 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^2 z^{10}+4 z^{10}+12 a^3 z^9+20 a z^9+8 z^9 a^{-1} +13 a^4 z^8+18 a^2 z^8+5 z^8 a^{-2} +10 z^8+6 a^5 z^7-16 a^3 z^7-32 a z^7-9 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-26 a^4 z^6-53 a^2 z^6+2 z^6 a^{-2} -24 z^6-8 a^5 z^5-8 a^3 z^5+2 a z^5+11 z^5 a^{-1} +9 z^5 a^{-3} +10 a^4 z^4+24 a^2 z^4-3 z^4 a^{-2} +3 z^4 a^{-4} +8 z^4+6 a^3 z^3+8 a z^3-6 z^3 a^{-1} -8 z^3 a^{-3} +2 a^4 z^2+5 a^2 z^2+z^2 a^{-2} -z^2 a^{-4} +5 z^2+2 a^5 z+2 a^3 z-2 a^4-4 a^2-1 }[/math] |
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