K12a449
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-10 q^2+17 q-24+28 q^{-1} -29 q^{-2} +27 q^{-3} -21 q^{-4} +14 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-16 t^2+45 t-61+45 t^{-1} -16 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^4-z^2+1 }[/math] |
| Determinant | 187 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8+3 z^2 a^6+2 a^6-3 z^4 a^4-2 z^2 a^4+z^6 a^2-z^4 a^2-3 z^2 a^2-a^2+z^6+z^4+z^2-z^4 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+13 a^2 z^{10}+7 z^{10}+8 a^5 z^9+14 a^3 z^9+15 a z^9+9 z^9 a^{-1} +7 a^6 z^8-3 a^4 z^8-27 a^2 z^8+5 z^8 a^{-2} -12 z^8+5 a^7 z^7-11 a^5 z^7-49 a^3 z^7-63 a z^7-29 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-7 a^6 z^6-9 a^4 z^6+4 a^2 z^6-15 z^6 a^{-2} -12 z^6+a^9 z^5-5 a^7 z^5+9 a^5 z^5+57 a^3 z^5+70 a z^5+26 z^5 a^{-1} -2 z^5 a^{-3} -5 a^8 z^4+12 a^4 z^4+18 a^2 z^4+10 z^4 a^{-2} +21 z^4-2 a^9 z^3-4 a^5 z^3-30 a^3 z^3-31 a z^3-7 z^3 a^{-1} +3 a^8 z^2+5 a^6 z^2-4 a^4 z^2-12 a^2 z^2+z^2 a^{-2} -5 z^2+a^9 z+a^7 z+2 a^5 z+6 a^3 z+4 a z-a^8-2 a^6+a^2- a^{-2} }[/math] |
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