K12a326
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+18 q^7-26 q^6+32 q^5-34 q^4+32 q^3-26 q^2+18 q-9+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-19 t^2+51 t-69+51 t^{-1} -19 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^4 a^{-2} +4 z^4 a^{-4} -5 z^4 a^{-6} -z^4+2 z^2 a^{-2} +5 z^2 a^{-4} -8 z^2 a^{-6} +4 z^2 a^{-8} -z^2+ a^{-2} +2 a^{-4} -4 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +8 z^{10} a^{-4} +14 z^{10} a^{-6} +6 z^{10} a^{-8} +13 z^9 a^{-3} +23 z^9 a^{-5} +17 z^9 a^{-7} +7 z^9 a^{-9} +12 z^8 a^{-2} +3 z^8 a^{-4} -17 z^8 a^{-6} -4 z^8 a^{-8} +4 z^8 a^{-10} +8 z^7 a^{-1} -19 z^7 a^{-3} -67 z^7 a^{-5} -59 z^7 a^{-7} -18 z^7 a^{-9} +z^7 a^{-11} -16 z^6 a^{-2} -33 z^6 a^{-4} -26 z^6 a^{-6} -25 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6+a z^5-9 z^5 a^{-1} +13 z^5 a^{-3} +65 z^5 a^{-5} +57 z^5 a^{-7} +12 z^5 a^{-9} -3 z^5 a^{-11} +8 z^4 a^{-2} +36 z^4 a^{-4} +45 z^4 a^{-6} +34 z^4 a^{-8} +12 z^4 a^{-10} -5 z^4-a z^3+3 z^3 a^{-1} -5 z^3 a^{-3} -30 z^3 a^{-5} -26 z^3 a^{-7} -2 z^3 a^{-9} +3 z^3 a^{-11} +z^2 a^{-2} -14 z^2 a^{-4} -24 z^2 a^{-6} -16 z^2 a^{-8} -5 z^2 a^{-10} +2 z^2+2 z a^{-3} +5 z a^{-5} +5 z a^{-7} +z a^{-9} -z a^{-11} - a^{-2} +2 a^{-4} +4 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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