K12n518
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+7 q^{13}-9 q^{12}+11 q^{11}-12 q^{10}+9 q^9-7 q^8+4 q^7+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^2+16 t-21+16 t^{-1} -6 t^{-2} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+8 z^6+14 z^4+8 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +8 z^6 a^{-8} +20 z^4 a^{-8} -4 z^4 a^{-10} -2 z^4 a^{-12} +20 z^2 a^{-8} -11 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +7 a^{-8} -8 a^{-10} +2 a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-12} +z^{10} a^{-14} +z^9 a^{-11} +5 z^9 a^{-13} +4 z^9 a^{-15} +z^8 a^{-8} -3 z^8 a^{-12} +4 z^8 a^{-14} +6 z^8 a^{-16} -6 z^7 a^{-11} -20 z^7 a^{-13} -10 z^7 a^{-15} +4 z^7 a^{-17} -8 z^6 a^{-8} -4 z^6 a^{-10} +2 z^6 a^{-12} -22 z^6 a^{-14} -19 z^6 a^{-16} +z^6 a^{-18} -4 z^5 a^{-9} +12 z^5 a^{-11} +30 z^5 a^{-13} +3 z^5 a^{-15} -11 z^5 a^{-17} +20 z^4 a^{-8} +18 z^4 a^{-10} +7 z^4 a^{-12} +24 z^4 a^{-14} +13 z^4 a^{-16} -2 z^4 a^{-18} +12 z^3 a^{-9} +2 z^3 a^{-11} -14 z^3 a^{-13} +4 z^3 a^{-17} -20 z^2 a^{-8} -21 z^2 a^{-10} -4 z^2 a^{-12} -5 z^2 a^{-14} -2 z^2 a^{-16} -8 z a^{-9} -8 z a^{-11} +7 a^{-8} +8 a^{-10} +2 a^{-12} }[/math] |
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