K12a728
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-6 q^5+10 q^4-15 q^3+19 q^2-20 q+20-16 q^{-1} +12 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+17 t^2-25 t+29-25 t^{-1} +17 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+9 z^4+3 z^2+1 }[/math] |
| Determinant | 133 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+8 z^4 a^{-2} -4 z^4 a^{-4} +9 z^4-5 a^2 z^2+4 z^2 a^{-2} -4 z^2 a^{-4} +8 z^2-2 a^2- a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+5 a z^9+6 z^9 a^{-1} +5 z^9 a^{-3} +4 z^9 a^{-5} +6 a^2 z^8-14 z^8 a^{-2} -6 z^8 a^{-4} +3 z^8 a^{-6} +z^8+5 a^3 z^7-5 a z^7-18 z^7 a^{-1} -23 z^7 a^{-3} -14 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-9 a^2 z^6+10 z^6 a^{-2} -3 z^6 a^{-4} -12 z^6 a^{-6} -11 z^6+a^5 z^5-7 a^3 z^5+a z^5+18 z^5 a^{-1} +26 z^5 a^{-3} +13 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4+8 a^2 z^4-2 z^4 a^{-2} +6 z^4 a^{-4} +13 z^4 a^{-6} +18 z^4-2 a^5 z^3+2 a^3 z^3+2 a z^3-5 z^3 a^{-1} -11 z^3 a^{-3} -4 z^3 a^{-5} +4 z^3 a^{-7} +2 a^4 z^2-7 a^2 z^2-4 z^2 a^{-6} -13 z^2+a^5 z-2 a z-z a^{-1} +z a^{-3} -z a^{-7} +2 a^2- a^{-4} +4 }[/math] |
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