K12a490
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+10 q^{13}-18 q^{12}+25 q^{11}-32 q^{10}+33 q^9-30 q^8+25 q^7-16 q^6+9 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 7 t^3-25 t^2+45 t-53+45 t^{-1} -25 t^{-2} +7 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 7 z^6+17 z^4+8 z^2+1 }[/math] |
| Determinant | 207 |
| 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} +9 z^4 a^{-10} -4 z^4 a^{-12} +3 z^2 a^{-6} +7 z^2 a^{-8} +7 z^2 a^{-10} -10 z^2 a^{-12} +z^2 a^{-14} + a^{-6} +2 a^{-8} + a^{-10} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +13 z^{10} a^{-12} +7 z^{10} a^{-14} +7 z^9 a^{-9} +14 z^9 a^{-11} +17 z^9 a^{-13} +10 z^9 a^{-15} +6 z^8 a^{-8} -4 z^8 a^{-10} -21 z^8 a^{-12} -3 z^8 a^{-14} +8 z^8 a^{-16} +3 z^7 a^{-7} -8 z^7 a^{-9} -39 z^7 a^{-11} -51 z^7 a^{-13} -19 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -12 z^6 a^{-8} -z^6 a^{-10} +13 z^6 a^{-12} -16 z^6 a^{-14} -16 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} -3 z^5 a^{-9} +43 z^5 a^{-11} +60 z^5 a^{-13} +12 z^5 a^{-15} -8 z^5 a^{-17} -3 z^4 a^{-6} +10 z^4 a^{-8} -4 z^4 a^{-10} -10 z^4 a^{-12} +18 z^4 a^{-14} +9 z^4 a^{-16} -2 z^4 a^{-18} +3 z^3 a^{-7} +7 z^3 a^{-9} -24 z^3 a^{-11} -38 z^3 a^{-13} -6 z^3 a^{-15} +4 z^3 a^{-17} +3 z^2 a^{-6} -6 z^2 a^{-8} +3 z^2 a^{-10} +12 z^2 a^{-12} -4 z^2 a^{-14} -3 z^2 a^{-16} +z^2 a^{-18} -4 z a^{-9} +5 z a^{-11} +13 z a^{-13} +3 z a^{-15} -z a^{-17} - a^{-6} +2 a^{-8} - a^{-10} -5 a^{-12} -2 a^{-14} }[/math] |
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