K12a866
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-24+36 q^{-1} -44 q^{-2} +48 q^{-3} -44 q^{-4} +36 q^{-5} -25 q^{-6} +13 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-34 t^2+62 t-75+62 t^{-1} -34 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-4 z^6-2 z^4+2 z^2+1 }[/math] |
| Determinant | 295 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-3 a^4 z^6-3 a^2 z^6+z^6+2 a^6 z^4-3 a^4 z^4-3 a^2 z^4+2 z^4+a^6 z^2+z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^5 z^{11}+5 a^3 z^{11}+14 a^6 z^{10}+28 a^4 z^{10}+14 a^2 z^{10}+17 a^7 z^9+25 a^5 z^9+25 a^3 z^9+17 a z^9+12 a^8 z^8-11 a^6 z^8-47 a^4 z^8-12 a^2 z^8+12 z^8+5 a^9 z^7-28 a^7 z^7-67 a^5 z^7-69 a^3 z^7-30 a z^7+5 z^7 a^{-1} +a^{10} z^6-20 a^8 z^6-11 a^6 z^6+21 a^4 z^6-11 a^2 z^6+z^6 a^{-2} -21 z^6-7 a^9 z^5+14 a^7 z^5+49 a^5 z^5+53 a^3 z^5+18 a z^5-7 z^5 a^{-1} -a^{10} z^4+11 a^8 z^4+7 a^6 z^4-7 a^4 z^4+11 a^2 z^4-z^4 a^{-2} +12 z^4+3 a^9 z^3-2 a^7 z^3-16 a^5 z^3-17 a^3 z^3-4 a z^3+2 z^3 a^{-1} -a^8 z^2-a^6 z^2+2 a^4 z^2-2 z^2-a^7 z+a^5 z+3 a^3 z+a z+a^6+a^4-a^2 }[/math] |
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