K12n857
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-10 q^2+16 q-21+23 q^{-1} -22 q^{-2} +19 q^{-3} -13 q^{-4} +7 q^{-5} -2 q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-17 t^2+29 t-33+29 t^{-1} -17 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6-z^4-z^2+1 }[/math] |
| Determinant | 139 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-5 a^2 z^6+2 z^6+4 a^4 z^4-10 a^2 z^4-z^4 a^{-2} +6 z^4-a^6 z^2+6 a^4 z^2-9 a^2 z^2-z^2 a^{-2} +4 z^2-a^6+3 a^4-2 a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^2 z^{10}+4 z^{10}+11 a^3 z^9+19 a z^9+8 z^9 a^{-1} +12 a^4 z^8+10 a^2 z^8+5 z^8 a^{-2} +3 z^8+6 a^5 z^7-22 a^3 z^7-53 a z^7-24 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-26 a^4 z^6-49 a^2 z^6-15 z^6 a^{-2} -37 z^6-3 a^5 z^5+14 a^3 z^5+37 a z^5+18 z^5 a^{-1} -2 z^5 a^{-3} +8 a^6 z^4+29 a^4 z^4+43 a^2 z^4+12 z^4 a^{-2} +34 z^4+3 a^7 z^3+4 a^5 z^3-6 a^3 z^3-9 a z^3-z^3 a^{-1} +z^3 a^{-3} -5 a^6 z^2-15 a^4 z^2-16 a^2 z^2-6 z^2-a^7 z-a^5 z+a^3 z-z a^{-1} +a^6+3 a^4+2 a^2- a^{-2} }[/math] |
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