K12a66
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+19 q^4-28 q^3+35 q^2-38 q+36-29 q^{-1} +21 q^{-2} -11 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+25 t^2-52 t+67-52 t^{-1} +25 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 237 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-10 z^4 a^{-2} +3 z^4 a^{-4} +13 z^4-5 a^2 z^2-14 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +15 z^2-2 a^2-7 a^{-2} +4 a^{-4} - a^{-6} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +6 z^{10} a^{-4} +9 z^{10}+17 a z^9+30 z^9 a^{-1} +20 z^9 a^{-3} +7 z^9 a^{-5} +17 a^2 z^8-8 z^8 a^{-2} -z^8 a^{-4} +4 z^8 a^{-6} +14 z^8+10 a^3 z^7-23 a z^7-76 z^7 a^{-1} -61 z^7 a^{-3} -17 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-30 a^2 z^6-57 z^6 a^{-2} -32 z^6 a^{-4} -12 z^6 a^{-6} -71 z^6+a^5 z^5-12 a^3 z^5+6 a z^5+53 z^5 a^{-1} +48 z^5 a^{-3} +11 z^5 a^{-5} -3 z^5 a^{-7} -3 a^4 z^4+30 a^2 z^4+77 z^4 a^{-2} +43 z^4 a^{-4} +13 z^4 a^{-6} +80 z^4-a^5 z^3+8 a^3 z^3+7 a z^3-12 z^3 a^{-1} -13 z^3 a^{-3} +3 z^3 a^{-7} -15 a^2 z^2-39 z^2 a^{-2} -21 z^2 a^{-4} -6 z^2 a^{-6} -39 z^2-2 a^3 z-3 a z+z a^{-3} -z a^{-5} -z a^{-7} +2 a^2+7 a^{-2} +4 a^{-4} + a^{-6} +7 }[/math] |
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