K12a418
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+21 q-30+37 q^{-1} -39 q^{-2} +37 q^{-3} -29 q^{-4} +20 q^{-5} -11 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+54 t-67+54 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+2 z^2+1 }[/math] |
| Determinant | 247 |
| 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^4-8 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+8 a^4 z^2-7 a^2 z^2-z^2 a^{-2} +4 z^2-2 a^6+4 a^4-2 a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+11 a^4 z^{10}+20 a^2 z^{10}+9 z^{10}+17 a^5 z^9+29 a^3 z^9+22 a z^9+10 z^9 a^{-1} +16 a^6 z^8+a^4 z^8-31 a^2 z^8+5 z^8 a^{-2} -11 z^8+10 a^7 z^7-25 a^5 z^7-89 a^3 z^7-82 a z^7-27 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-26 a^6 z^6-41 a^4 z^6-20 a^2 z^6-13 z^6 a^{-2} -22 z^6+a^9 z^5-13 a^7 z^5+12 a^5 z^5+84 a^3 z^5+81 a z^5+21 z^5 a^{-1} -2 z^5 a^{-3} -3 a^8 z^4+22 a^6 z^4+47 a^4 z^4+45 a^2 z^4+10 z^4 a^{-2} +33 z^4-a^9 z^3+9 a^7 z^3+a^5 z^3-33 a^3 z^3-31 a z^3-6 z^3 a^{-1} +z^3 a^{-3} -10 a^6 z^2-21 a^4 z^2-19 a^2 z^2-3 z^2 a^{-2} -11 z^2-3 a^7 z-2 a^5 z+4 a^3 z+4 a z+z a^{-1} +2 a^6+4 a^4+2 a^2+1 }[/math] |
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