K12n423
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-4 q^2+5 q-4+3 q^{-1} -2 q^{-2} +2 q^{-4} -2 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-3 t^2+3 t-1+3 t^{-1} -3 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+3 z^4+1 }[/math] |
| Determinant | 15 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4+3 z^2 a^4+3 a^4-z^4 a^2-4 z^2 a^2-3 a^2+z^6+4 z^4+4 z^2+2-z^4 a^{-2} -2 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^5 z^9+2 a^3 z^9+4 a z^9+3 z^9 a^{-1} +2 a^6 z^8+2 a^4 z^8-4 a^2 z^8+3 z^8 a^{-2} -z^8+a^7 z^7-5 a^5 z^7-15 a^3 z^7-24 a z^7-14 z^7 a^{-1} +z^7 a^{-3} -11 a^6 z^6-15 a^4 z^6-6 a^2 z^6-14 z^6 a^{-2} -16 z^6-5 a^7 z^5+4 a^5 z^5+29 a^3 z^5+39 a z^5+15 z^5 a^{-1} -4 z^5 a^{-3} +16 a^6 z^4+26 a^4 z^4+23 a^2 z^4+16 z^4 a^{-2} +29 z^4+6 a^7 z^3-a^5 z^3-23 a^3 z^3-25 a z^3-6 z^3 a^{-1} +3 z^3 a^{-3} -8 a^6 z^2-17 a^4 z^2-17 a^2 z^2-6 z^2 a^{-2} -14 z^2-a^7 z+a^5 z+7 a^3 z+7 a z+2 z a^{-1} +a^6+3 a^4+3 a^2+2 }[/math] |
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