K12a222
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-23 q^3+34 q^2-42 q+45-42 q^{-1} +34 q^{-2} -23 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-62 t+81-62 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4-2 z^2+1 }[/math] |
| Determinant | 281 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-5 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +9 z^4+a^4 z^2-6 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} +8 z^2+a^4-2 a^2-2 a^{-2} + a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +11 a^2 z^{10}+11 z^{10} a^{-2} +22 z^{10}+16 a^3 z^9+34 a z^9+34 z^9 a^{-1} +16 z^9 a^{-3} +12 a^4 z^8+3 a^2 z^8+3 z^8 a^{-2} +12 z^8 a^{-4} -18 z^8+5 a^5 z^7-28 a^3 z^7-91 a z^7-91 z^7 a^{-1} -28 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-45 a^2 z^6-45 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -44 z^6-7 a^5 z^5+17 a^3 z^5+79 a z^5+79 z^5 a^{-1} +17 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+14 a^4 z^4+46 a^2 z^4+46 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +62 z^4+2 a^5 z^3-7 a^3 z^3-29 a z^3-29 z^3 a^{-1} -7 z^3 a^{-3} +2 z^3 a^{-5} -5 a^4 z^2-17 a^2 z^2-17 z^2 a^{-2} -5 z^2 a^{-4} -24 z^2+2 a^3 z+4 a z+4 z a^{-1} +2 z a^{-3} +a^4+2 a^2+2 a^{-2} + a^{-4} +3 }[/math] |
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