K12a86
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+15 q^{-1} -21 q^{-2} +26 q^{-3} -26 q^{-4} +25 q^{-5} -19 q^{-6} +13 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-17 t^2+39 t-51+39 t^{-1} -17 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+7 z^4+7 z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-2 a^8+z^6 a^6+2 z^4 a^6+2 z^2 a^6+2 z^6 a^4+6 z^4 a^4+9 z^2 a^4+5 a^4+z^6 a^2+z^4 a^2-z^2 a^2-2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+9 z^4 a^{10}-2 z^2 a^{10}+5 z^9 a^9-16 z^7 a^9+17 z^5 a^9-12 z^3 a^9+6 z a^9+4 z^{10} a^8-6 z^8 a^8-6 z^6 a^8+8 z^4 a^8-2 a^8+z^{11} a^7+12 z^9 a^7-45 z^7 a^7+57 z^5 a^7-39 z^3 a^7+12 z a^7+8 z^{10} a^6-8 z^8 a^6-21 z^6 a^6+36 z^4 a^6-17 z^2 a^6+z^{11} a^5+15 z^9 a^5-40 z^7 a^5+36 z^5 a^5-14 z^3 a^5+3 z a^5+4 z^{10} a^4+11 z^8 a^4-44 z^6 a^4+52 z^4 a^4-26 z^2 a^4+5 a^4+8 z^9 a^3-4 z^7 a^3-13 z^5 a^3+15 z^3 a^3-3 z a^3+10 z^8 a^2-15 z^6 a^2+10 z^4 a^2-6 z^2 a^2+2 a^2+8 z^7 a-12 z^5 a+6 z^3 a-2 z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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