K12a1049
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+18 q-25+32 q^{-1} -34 q^{-2} +32 q^{-3} -26 q^{-4} +18 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-27 t^2+45 t-51+45 t^{-1} -27 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+7 z^4+2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-3 a^2 z^6+2 z^6-a^6 z^4+5 a^4 z^4-a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+a^4 z^2+4 a^2 z^2-2 z^2 a^{-2} +z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+17 a^2 z^{10}+8 z^{10}+13 a^5 z^9+16 a^3 z^9+11 a z^9+8 z^9 a^{-1} +13 a^6 z^8-4 a^4 z^8-40 a^2 z^8+4 z^8 a^{-2} -19 z^8+9 a^7 z^7-16 a^5 z^7-51 a^3 z^7-52 a z^7-25 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-19 a^6 z^6-15 a^4 z^6+30 a^2 z^6-12 z^6 a^{-2} +10 z^6+a^9 z^5-12 a^7 z^5+2 a^5 z^5+45 a^3 z^5+58 a z^5+25 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+12 a^6 z^4+12 a^4 z^4-17 a^2 z^4+10 z^4 a^{-2} -3 z^4-a^9 z^3+7 a^7 z^3+5 a^5 z^3-15 a^3 z^3-26 a z^3-12 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-4 a^6 z^2+a^4 z^2+13 a^2 z^2-3 z^2 a^{-2} +4 z^2-2 a^7 z-2 a^5 z+2 a^3 z+4 a z+2 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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