K12a293
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-5 q^{14}+12 q^{13}-21 q^{12}+29 q^{11}-35 q^{10}+36 q^9-33 q^8+26 q^7-16 q^6+9 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 7 t^3-26 t^2+50 t-61+50 t^{-1} -26 t^{-2} +7 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 7 z^6+16 z^4+9 z^2+1 }[/math] |
| Determinant | 227 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +3 z^6 a^{-10} +3 z^4 a^{-6} +9 z^4 a^{-8} +8 z^4 a^{-10} -4 z^4 a^{-12} +3 z^2 a^{-6} +8 z^2 a^{-8} +5 z^2 a^{-10} -8 z^2 a^{-12} +z^2 a^{-14} + a^{-6} +2 a^{-8} -3 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +14 z^{10} a^{-12} +8 z^{10} a^{-14} +7 z^9 a^{-9} +17 z^9 a^{-11} +23 z^9 a^{-13} +13 z^9 a^{-15} +6 z^8 a^{-8} -z^8 a^{-10} -14 z^8 a^{-12} +4 z^8 a^{-14} +11 z^8 a^{-16} +3 z^7 a^{-7} -7 z^7 a^{-9} -42 z^7 a^{-11} -58 z^7 a^{-13} -21 z^7 a^{-15} +5 z^7 a^{-17} +z^6 a^{-6} -12 z^6 a^{-8} -8 z^6 a^{-10} -9 z^6 a^{-12} -36 z^6 a^{-14} -21 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} -4 z^5 a^{-9} +38 z^5 a^{-11} +49 z^5 a^{-13} +5 z^5 a^{-15} -8 z^5 a^{-17} -3 z^4 a^{-6} +11 z^4 a^{-8} +5 z^4 a^{-10} +8 z^4 a^{-12} +29 z^4 a^{-14} +11 z^4 a^{-16} -z^4 a^{-18} +3 z^3 a^{-7} +9 z^3 a^{-9} -14 z^3 a^{-11} -22 z^3 a^{-13} +z^3 a^{-15} +3 z^3 a^{-17} +3 z^2 a^{-6} -7 z^2 a^{-8} +6 z^2 a^{-12} -6 z^2 a^{-14} -2 z^2 a^{-16} -4 z a^{-9} +z a^{-11} +5 z a^{-13} - a^{-6} +2 a^{-8} -3 a^{-12} - a^{-14} }[/math] |
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