K12a995
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+10 q^{13}-19 q^{12}+27 q^{11}-34 q^{10}+36 q^9-34 q^8+28 q^7-18 q^6+11 q^5-4 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^3-28 t^2+49 t-57+49 t^{-1} -28 t^{-2} +8 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^6+20 z^4+9 z^2+1 }[/math] |
| Determinant | 227 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +4 z^6 a^{-8} +3 z^6 a^{-10} +2 z^4 a^{-6} +14 z^4 a^{-8} +8 z^4 a^{-10} -4 z^4 a^{-12} +14 z^2 a^{-8} +4 z^2 a^{-10} -10 z^2 a^{-12} +z^2 a^{-14} +4 a^{-8} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-11} +3 z^{11} a^{-13} +10 z^{10} a^{-10} +18 z^{10} a^{-12} +8 z^{10} a^{-14} +13 z^9 a^{-9} +18 z^9 a^{-11} +15 z^9 a^{-13} +10 z^9 a^{-15} +10 z^8 a^{-8} -16 z^8 a^{-10} -40 z^8 a^{-12} -6 z^8 a^{-14} +8 z^8 a^{-16} +4 z^7 a^{-7} -32 z^7 a^{-9} -65 z^7 a^{-11} -49 z^7 a^{-13} -16 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -26 z^6 a^{-8} +4 z^6 a^{-10} +41 z^6 a^{-12} -6 z^6 a^{-14} -15 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +27 z^5 a^{-9} +81 z^5 a^{-11} +62 z^5 a^{-13} +7 z^5 a^{-15} -8 z^5 a^{-17} -2 z^4 a^{-6} +25 z^4 a^{-8} +6 z^4 a^{-10} -28 z^4 a^{-12} +3 z^4 a^{-14} +8 z^4 a^{-16} -2 z^4 a^{-18} -4 z^3 a^{-9} -40 z^3 a^{-11} -45 z^3 a^{-13} -4 z^3 a^{-15} +5 z^3 a^{-17} -14 z^2 a^{-8} +16 z^2 a^{-12} -z^2 a^{-16} +z^2 a^{-18} -3 z a^{-9} +7 z a^{-11} +13 z a^{-13} +2 z a^{-15} -z a^{-17} +4 a^{-8} -5 a^{-12} -2 a^{-14} }[/math] |
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