K12n422
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-13 q^3+18 q^2-19 q+19-16 q^{-1} +11 q^{-2} -6 q^{-3} +2 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+11 t^2-27 t+37-27 t^{-1} +11 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^4-z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -z^4-a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+11 z^9 a^{-1} +6 z^9 a^{-3} +4 a^2 z^8+9 z^8 a^{-2} +7 z^8 a^{-4} +6 z^8+a^3 z^7-11 a z^7-27 z^7 a^{-1} -11 z^7 a^{-3} +4 z^7 a^{-5} -6 a^2 z^6-36 z^6 a^{-2} -19 z^6 a^{-4} +z^6 a^{-6} -22 z^6+5 a^3 z^5+22 a z^5+28 z^5 a^{-1} +z^5 a^{-3} -10 z^5 a^{-5} +3 a^4 z^4+12 a^2 z^4+38 z^4 a^{-2} +15 z^4 a^{-4} -2 z^4 a^{-6} +30 z^4-8 a^3 z^3-20 a z^3-15 z^3 a^{-1} +2 z^3 a^{-3} +5 z^3 a^{-5} -4 a^4 z^2-11 a^2 z^2-14 z^2 a^{-2} -5 z^2 a^{-4} -16 z^2+3 a^3 z+6 a z+4 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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