K12a1203
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+12 q-16+21 q^{-1} -22 q^{-2} +21 q^{-3} -17 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-18 t^2+25 t-27+25 t^{-1} -18 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+12 z^4+4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+25 a^2 z^6-6 z^6-13 a^4 z^4+38 a^2 z^4-13 z^4-12 a^4 z^2+28 a^2 z^2-12 z^2-4 a^4+8 a^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+10 a^2 z^{10}+5 z^{10}+7 a^5 z^9+3 a^3 z^9+a z^9+5 z^9 a^{-1} +7 a^6 z^8-9 a^4 z^8-38 a^2 z^8+3 z^8 a^{-2} -19 z^8+5 a^7 z^7-15 a^5 z^7-20 a^3 z^7-20 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-14 a^6 z^6+6 a^4 z^6+66 a^2 z^6-11 z^6 a^{-2} +32 z^6+a^9 z^5-7 a^7 z^5+14 a^5 z^5+30 a^3 z^5+36 a z^5+24 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+13 a^6 z^4-a^4 z^4-66 a^2 z^4+10 z^4 a^{-2} -37 z^4-2 a^9 z^3+a^7 z^3-a^5 z^3-16 a^3 z^3-32 a z^3-16 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-6 a^6 z^2+9 a^4 z^2+35 a^2 z^2-z^2 a^{-2} +18 z^2+a^9 z-a^7 z-a^5 z+5 a^3 z+8 a z+4 z a^{-1} -4 a^4-8 a^2-3 }[/math] |
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