K12n844
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+6 q^3-8 q^2+11 q-12+11 q^{-1} -10 q^{-2} +7 q^{-3} -4 q^{-4} +2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-12 t^2+16 t-13+16 t^{-1} -12 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+6 z^4-5 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-z^4 a^4-3 z^2 a^4+z^6 a^2+2 z^4 a^2-3 z^2 a^2-3 a^2+2 z^6+8 z^4+9 z^2+5-3 z^4 a^{-2} -9 z^2 a^{-2} -4 a^{-2} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+6 a z^9+9 z^9 a^{-1} +3 z^9 a^{-3} +7 a^2 z^8-4 z^8 a^{-2} +z^8 a^{-4} +2 z^8+5 a^3 z^7-20 a z^7-40 z^7 a^{-1} -15 z^7 a^{-3} +3 a^4 z^6-20 a^2 z^6-14 z^6 a^{-2} -5 z^6 a^{-4} -32 z^6+a^5 z^5-6 a^3 z^5+23 a z^5+53 z^5 a^{-1} +23 z^5 a^{-3} -a^4 z^4+19 a^2 z^4+37 z^4 a^{-2} +9 z^4 a^{-4} +48 z^4+3 a^5 z^3-6 a^3 z^3-23 a z^3-25 z^3 a^{-1} -11 z^3 a^{-3} +3 a^6 z^2-15 a^2 z^2-22 z^2 a^{-2} -7 z^2 a^{-4} -27 z^2+6 a^3 z+9 a z+5 z a^{-1} +2 z a^{-3} -a^6+3 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
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