K12n246
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+9 q^2-11 q+12-10 q^{-1} +9 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-17 t+25-17 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4+3 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^4-a^4+z^4 a^2+3 z^4+6 z^2+4+z^4 a^{-2} -z^2 a^{-2} -2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+4 a z^9+3 z^9 a^{-1} -4 a^2 z^8+5 z^8 a^{-2} +z^8-5 a^3 z^7-16 a z^7-6 z^7 a^{-1} +5 z^7 a^{-3} +2 a^4 z^6+10 a^2 z^6-13 z^6 a^{-2} +3 z^6 a^{-4} -8 z^6+a^5 z^5+16 a^3 z^5+33 a z^5+5 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} -5 a^4 z^4-5 a^2 z^4+14 z^4 a^{-2} -6 z^4 a^{-4} +20 z^4-4 a^5 z^3-21 a^3 z^3-25 a z^3+2 z^3 a^{-1} +8 z^3 a^{-3} -2 z^3 a^{-5} +3 a^4 z^2-4 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -15 z^2+4 a^5 z+8 a^3 z+5 a z-z a^{-1} -2 z a^{-3} -a^4+2 a^{-2} +4 }[/math] |
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