K12n657
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-7 q^3+10 q^2-13 q+14-12 q^{-1} +10 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+9 t^2-16 t+21-16 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+5 z^4+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-4 z^4 a^{-2} +13 z^4-5 a^2 z^2-6 z^2 a^{-2} +11 z^2-a^2-3 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+4 a z^9+5 z^9 a^{-1} +z^9 a^{-3} +6 a^2 z^8-z^8 a^{-2} +5 z^8+5 a^3 z^7-9 a z^7-15 z^7 a^{-1} -z^7 a^{-3} +3 a^4 z^6-17 a^2 z^6+2 z^6 a^{-2} +4 z^6 a^{-4} -22 z^6+a^5 z^5-11 a^3 z^5+9 a z^5+24 z^5 a^{-1} +4 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4+21 a^2 z^4+2 z^4 a^{-2} -8 z^4 a^{-4} +37 z^4-2 a^5 z^3+6 a^3 z^3-16 z^3 a^{-1} -10 z^3 a^{-3} -2 z^3 a^{-5} +a^4 z^2-10 a^2 z^2-9 z^2 a^{-2} +z^2 a^{-4} -21 z^2-a^3 z+4 z a^{-1} +4 z a^{-3} +z a^{-5} +a^2+3 a^{-2} + a^{-4} +4 }[/math] |
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