K12a703
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-27+38 q^{-1} -45 q^{-2} +47 q^{-3} -42 q^{-4} +33 q^{-5} -21 q^{-6} +10 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-32 t^2+64 t-79+64 t^{-1} -32 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 291 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-6 z^2 a^6-4 a^6+3 z^6 a^4+8 z^4 a^4+9 z^2 a^4+5 a^4-z^8 a^2-3 z^6 a^2-4 z^4 a^2-3 z^2 a^2-2 a^2+z^6+z^4+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^5 z^{11}+4 a^3 z^{11}+10 a^6 z^{10}+25 a^4 z^{10}+15 a^2 z^{10}+11 a^7 z^9+24 a^5 z^9+35 a^3 z^9+22 a z^9+8 a^8 z^8-2 a^6 z^8-30 a^4 z^8-4 a^2 z^8+16 z^8+4 a^9 z^7-13 a^7 z^7-61 a^5 z^7-88 a^3 z^7-38 a z^7+6 z^7 a^{-1} +a^{10} z^6-13 a^8 z^6-23 a^6 z^6-20 a^4 z^6-37 a^2 z^6+z^6 a^{-2} -25 z^6-8 a^9 z^5-a^7 z^5+42 a^5 z^5+55 a^3 z^5+15 a z^5-5 z^5 a^{-1} -2 a^{10} z^4+8 a^8 z^4+33 a^6 z^4+41 a^4 z^4+26 a^2 z^4+8 z^4+6 a^9 z^3+12 a^7 z^3-8 a^3 z^3-2 a z^3+a^{10} z^2-3 a^8 z^2-18 a^6 z^2-22 a^4 z^2-8 a^2 z^2-2 a^9 z-6 a^7 z-5 a^5 z-a^3 z+a^8+4 a^6+5 a^4+2 a^2+1 }[/math] |
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