K12a464
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+19 q^2-27 q+34-36 q^{-1} +33 q^{-2} -27 q^{-3} +19 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-49 t+63-49 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-10 a^2 z^4-3 z^4 a^{-2} +12 z^4-a^6 z^2+6 a^4 z^2-13 a^2 z^2-4 z^2 a^{-2} +12 z^2-a^6+4 a^4-6 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+14 a^2 z^{10}+8 z^{10}+7 a^5 z^9+18 a^3 z^9+25 a z^9+14 z^9 a^{-1} +4 a^6 z^8-2 a^4 z^8-10 a^2 z^8+14 z^8 a^{-2} +10 z^8+a^7 z^7-17 a^5 z^7-56 a^3 z^7-64 a z^7-17 z^7 a^{-1} +9 z^7 a^{-3} -12 a^6 z^6-30 a^4 z^6-45 a^2 z^6-22 z^6 a^{-2} +4 z^6 a^{-4} -53 z^6-3 a^7 z^5+10 a^5 z^5+43 a^3 z^5+46 a z^5+4 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+40 a^4 z^4+62 a^2 z^4+19 z^4 a^{-2} -4 z^4 a^{-4} +58 z^4+3 a^7 z^3+a^5 z^3-12 a^3 z^3-13 a z^3+4 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -6 a^6 z^2-20 a^4 z^2-32 a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} -27 z^2-a^7 z-a^5 z+2 a^3 z+2 a z-z a^{-1} -z a^{-3} +a^6+4 a^4+6 a^2+ a^{-2} +5 }[/math] |
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