K12a351
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+19 q^2-27 q+33-35 q^{-1} +33 q^{-2} -26 q^{-3} +18 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-48 t+61-48 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 221 |
| 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^2-12 a^2 z^2-4 z^2 a^{-2} +12 z^2-a^6+3 a^4-4 a^2- a^{-2} +4 }[/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+17 a^3 z^9+24 a z^9+14 z^9 a^{-1} +4 a^6 z^8-4 a^4 z^8-14 a^2 z^8+14 z^8 a^{-2} +8 z^8+a^7 z^7-18 a^5 z^7-56 a^3 z^7-64 a z^7-18 z^7 a^{-1} +9 z^7 a^{-3} -12 a^6 z^6-24 a^4 z^6-33 a^2 z^6-22 z^6 a^{-2} +4 z^6 a^{-4} -47 z^6-3 a^7 z^5+12 a^5 z^5+49 a^3 z^5+52 a z^5+6 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+33 a^4 z^4+50 a^2 z^4+18 z^4 a^{-2} -4 z^4 a^{-4} +51 z^4+3 a^7 z^3-a^5 z^3-18 a^3 z^3-19 a z^3+2 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -5 a^6 z^2-15 a^4 z^2-25 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -23 z^2-a^7 z+3 a^3 z+2 a z-z a^{-1} -z a^{-3} +a^6+3 a^4+4 a^2+ a^{-2} +4 }[/math] |
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