K12a637
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+20 q-28+35 q^{-1} -36 q^{-2} +34 q^{-3} -27 q^{-4} +18 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-26 t^2+50 t-61+50 t^{-1} -26 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+2 z^4+2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-7 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+6 a^4 z^2-4 a^2 z^2-z^2 a^{-2} +3 z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+18 a^2 z^{10}+9 z^{10}+13 a^5 z^9+20 a^3 z^9+17 a z^9+10 z^9 a^{-1} +13 a^6 z^8+a^4 z^8-32 a^2 z^8+5 z^8 a^{-2} -15 z^8+9 a^7 z^7-13 a^5 z^7-58 a^3 z^7-65 a z^7-28 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-18 a^6 z^6-27 a^4 z^6-2 a^2 z^6-13 z^6 a^{-2} -10 z^6+a^9 z^5-12 a^7 z^5-2 a^5 z^5+47 a^3 z^5+59 a z^5+21 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+12 a^6 z^4+25 a^4 z^4+20 a^2 z^4+9 z^4 a^{-2} +20 z^4-a^9 z^3+8 a^7 z^3+6 a^5 z^3-17 a^3 z^3-19 a z^3-4 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2-4 a^6 z^2-9 a^4 z^2-7 a^2 z^2-2 z^2 a^{-2} -5 z^2-2 a^7 z-a^5 z+3 a^3 z+3 a z+z a^{-1} +a^6+a^4-a^2 }[/math] |
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