K12a806
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+12 q-20+28 q^{-1} -33 q^{-2} +35 q^{-3} -31 q^{-4} +25 q^{-5} -16 q^{-6} +8 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-27 t^2+44 t-51+44 t^{-1} -27 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-z^4+3 z^2+1 }[/math] |
| Determinant | 219 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-4 a^4 z^6-3 a^2 z^6+z^6+3 a^6 z^4-5 a^4 z^4-a^2 z^4+2 z^4+a^6 z^2+2 a^2 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+7 a^6 z^{10}+16 a^4 z^{10}+9 a^2 z^{10}+8 a^7 z^9+8 a^5 z^9+13 a^3 z^9+13 a z^9+7 a^8 z^8-9 a^6 z^8-35 a^4 z^8-8 a^2 z^8+11 z^8+4 a^9 z^7-13 a^7 z^7-23 a^5 z^7-35 a^3 z^7-24 a z^7+5 z^7 a^{-1} +a^{10} z^6-16 a^8 z^6+3 a^6 z^6+37 a^4 z^6-6 a^2 z^6+z^6 a^{-2} -22 z^6-10 a^9 z^5+a^7 z^5+18 a^5 z^5+24 a^3 z^5+9 a z^5-8 z^5 a^{-1} -2 a^{10} z^4+11 a^8 z^4+5 a^6 z^4-19 a^4 z^4-z^4 a^{-2} +10 z^4+6 a^9 z^3+10 a^7 z^3+2 a^5 z^3-4 a^3 z^3+2 z^3 a^{-1} -2 a^8 z^2-6 a^6 z^2-a^4 z^2+3 a^2 z^2-4 a^7 z-5 a^5 z-a^3 z+2 a^6+3 a^4 }[/math] |
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