K12n872
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+15 q-19+22 q^{-1} -21 q^{-2} +18 q^{-3} -13 q^{-4} +7 q^{-5} -2 q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-16 t^2+27 t-31+27 t^{-1} -16 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^2+1 }[/math] |
| Determinant | 131 |
| 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} +7 z^4-a^6 z^2+6 a^4 z^2-10 a^2 z^2-2 z^2 a^{-2} +8 z^2-a^6+3 a^4-4 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{10}+3 z^{10}+10 a^3 z^9+16 a z^9+6 z^9 a^{-1} +12 a^4 z^8+14 a^2 z^8+4 z^8 a^{-2} +6 z^8+6 a^5 z^7-19 a^3 z^7-42 a z^7-16 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-28 a^4 z^6-59 a^2 z^6-13 z^6 a^{-2} -43 z^6-3 a^5 z^5+10 a^3 z^5+23 a z^5+7 z^5 a^{-1} -3 z^5 a^{-3} +8 a^6 z^4+33 a^4 z^4+59 a^2 z^4+14 z^4 a^{-2} +48 z^4+3 a^7 z^3+3 a^5 z^3-3 a^3 z^3-a z^3+5 z^3 a^{-1} +3 z^3 a^{-3} -5 a^6 z^2-17 a^4 z^2-26 a^2 z^2-6 z^2 a^{-2} -20 z^2-a^7 z-a^5 z-a z-2 z a^{-1} -z a^{-3} +a^6+3 a^4+4 a^2+ a^{-2} +4 }[/math] |
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