K12a881
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-4 q+7-9 q^{-1} +12 q^{-2} -12 q^{-3} +13 q^{-4} -11 q^{-5} +8 q^{-6} -6 q^{-7} +3 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+13 t^2-15 t+15-15 t^{-1} +13 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4 z^8+a^2 z^8-a^6 z^6+5 a^4 z^6+6 a^2 z^6-z^6-4 a^6 z^4+7 a^4 z^4+13 a^2 z^4-5 z^4-4 a^6 z^2+3 a^4 z^2+14 a^2 z^2-7 z^2-2 a^6+6 a^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}+3 z^4 a^{10}+6 z^5 a^9-5 z^3 a^9+2 z a^9+8 z^6 a^8-10 z^4 a^8+2 z^2 a^8+9 z^7 a^7-16 z^5 a^7+4 z^3 a^7-2 z a^7+9 z^8 a^6-23 z^6 a^6+14 z^4 a^6-7 z^2 a^6+2 a^6+7 z^9 a^5-20 z^7 a^5+9 z^5 a^5+3 z^3 a^5-2 z a^5+4 z^{10} a^4-10 z^8 a^4-5 z^6 a^4+14 z^4 a^4-z^2 a^4+z^{11} a^3+5 z^9 a^3-41 z^7 a^3+69 z^5 a^3-40 z^3 a^3+10 z a^3+6 z^{10} a^2-32 z^8 a^2+55 z^6 a^2-40 z^4 a^2+19 z^2 a^2-6 a^2+z^{11} a-z^9 a-19 z^7 a+55 z^5 a-50 z^3 a+14 z a+2 z^{10}-13 z^8+29 z^6-27 z^4+11 z^2-3+z^9 a^{-1} -7 z^7 a^{-1} +17 z^5 a^{-1} -17 z^3 a^{-1} +6 z a^{-1} }[/math] |
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