K12a364
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-24+35 q^{-1} -42 q^{-2} +46 q^{-3} -42 q^{-4} +34 q^{-5} -23 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+63 t-81+63 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+3 z^2+1 }[/math] |
| Determinant | 283 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-4 z^2 a^6-2 a^6+3 z^6 a^4+8 z^4 a^4+9 z^2 a^4+3 a^4-z^8 a^2-4 z^6 a^2-8 z^4 a^2-5 z^2 a^2+z^6+2 z^4+2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+10 a^6 z^{10}+21 a^4 z^{10}+11 a^2 z^{10}+14 a^7 z^9+31 a^5 z^9+33 a^3 z^9+16 a z^9+11 a^8 z^8+7 a^6 z^8-11 a^4 z^8+5 a^2 z^8+12 z^8+5 a^9 z^7-18 a^7 z^7-70 a^5 z^7-77 a^3 z^7-25 a z^7+5 z^7 a^{-1} +a^{10} z^6-19 a^8 z^6-46 a^6 z^6-49 a^4 z^6-45 a^2 z^6+z^6 a^{-2} -21 z^6-8 a^9 z^5+38 a^5 z^5+48 a^3 z^5+11 a z^5-7 z^5 a^{-1} -a^{10} z^4+12 a^8 z^4+41 a^6 z^4+51 a^4 z^4+38 a^2 z^4-z^4 a^{-2} +14 z^4+4 a^9 z^3+9 a^7 z^3+2 a^5 z^3-8 a^3 z^3-2 a z^3+3 z^3 a^{-1} -3 a^8 z^2-13 a^6 z^2-16 a^4 z^2-10 a^2 z^2-4 z^2-4 a^7 z-5 a^5 z-a^3 z+2 a^6+3 a^4 }[/math] |
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