K12n421
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-6 q^3+11 q^2-16 q+19-19 q^{-1} +18 q^{-2} -13 q^{-3} +8 q^{-4} -4 q^{-5} + q^{-6} }[/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{ -a^2 z^6-z^6+a^4 z^4-2 a^2 z^4+z^4 a^{-2} -z^4+a^4 z^2-2 a^2 z^2-z^2 a^{-2} +z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+6 a^3 z^9+11 a z^9+5 z^9 a^{-1} +7 a^4 z^8+9 a^2 z^8+4 z^8 a^{-2} +6 z^8+4 a^5 z^7-11 a^3 z^7-27 a z^7-11 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-19 a^4 z^6-36 a^2 z^6-6 z^6 a^{-2} -22 z^6-10 a^5 z^5+a^3 z^5+28 a z^5+22 z^5 a^{-1} +5 z^5 a^{-3} -2 a^6 z^4+15 a^4 z^4+38 a^2 z^4+12 z^4 a^{-2} +3 z^4 a^{-4} +30 z^4+5 a^5 z^3+2 a^3 z^3-15 a z^3-20 z^3 a^{-1} -8 z^3 a^{-3} -5 a^4 z^2-14 a^2 z^2-11 z^2 a^{-2} -4 z^2 a^{-4} -16 z^2+a^3 z+4 a z+6 z a^{-1} +3 z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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