K12a709
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+22 q-32+39 q^{-1} -41 q^{-2} +39 q^{-3} -31 q^{-4} +21 q^{-5} -11 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+57 t-71+57 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^2+1 }[/math] |
| Determinant | 259 |
| 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^4-9 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+9 a^4 z^2-10 a^2 z^2-z^2 a^{-2} +5 z^2-2 a^6+5 a^4-4 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+12 a^4 z^{10}+21 a^2 z^{10}+9 z^{10}+19 a^5 z^9+34 a^3 z^9+25 a z^9+10 z^9 a^{-1} +17 a^6 z^8+3 a^4 z^8-27 a^2 z^8+5 z^8 a^{-2} -8 z^8+10 a^7 z^7-30 a^5 z^7-100 a^3 z^7-87 a z^7-26 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-28 a^6 z^6-51 a^4 z^6-34 a^2 z^6-13 z^6 a^{-2} -28 z^6+a^9 z^5-12 a^7 z^5+19 a^5 z^5+92 a^3 z^5+83 a z^5+21 z^5 a^{-1} -2 z^5 a^{-3} -3 a^8 z^4+26 a^6 z^4+59 a^4 z^4+57 a^2 z^4+11 z^4 a^{-2} +38 z^4-a^9 z^3+8 a^7 z^3-3 a^5 z^3-39 a^3 z^3-34 a z^3-6 z^3 a^{-1} +z^3 a^{-3} -11 a^6 z^2-27 a^4 z^2-27 a^2 z^2-3 z^2 a^{-2} -14 z^2-2 a^7 z+6 a^3 z+5 a z+z a^{-1} +2 a^6+5 a^4+4 a^2+2 }[/math] |
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