K12n506
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+5 q^3-7 q^2+9 q-9+9 q^{-1} -7 q^{-2} +5 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-6 t^2+14 t-17+14 t^{-1} -6 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-z^2+1 }[/math] |
| Determinant | 59 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6-2 a^2 z^4-2 z^4 a^{-2} +4 z^4+a^4 z^2-5 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+3 a^3 z^9+8 a z^9+5 z^9 a^{-1} +a^4 z^8-6 a^2 z^8+5 z^8 a^{-2} -2 z^8-16 a^3 z^7-39 a z^7-20 z^7 a^{-1} +3 z^7 a^{-3} -5 a^4 z^6-6 a^2 z^6-18 z^6 a^{-2} +z^6 a^{-4} -20 z^6+26 a^3 z^5+56 a z^5+23 z^5 a^{-1} -7 z^5 a^{-3} +8 a^4 z^4+25 a^2 z^4+20 z^4 a^{-2} +z^4 a^{-4} +36 z^4-14 a^3 z^3-28 a z^3-13 z^3 a^{-1} +4 z^3 a^{-3} +3 z^3 a^{-5} -5 a^4 z^2-16 a^2 z^2-13 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -21 z^2+2 a^3 z+4 a z+2 z a^{-1} -z a^{-3} -z a^{-5} +a^4+3 a^2+3 a^{-2} + a^{-4} +5 }[/math] |
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