K12n305
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-2 q^{13}+2 q^{12}-4 q^{11}+4 q^{10}-4 q^9+4 q^8-3 q^7+3 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-4 t^3+4 t^2-3 t+3-3 t^{-1} +4 t^{-2} -4 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+12 z^6+20 z^4+9 z^2+1 }[/math] |
| Determinant | 29 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +6 z^6 a^{-10} -z^6 a^{-12} +16 z^4 a^{-8} +10 z^4 a^{-10} -6 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{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +3 z^9 a^{-11} +2 z^9 a^{-13} +z^8 a^{-8} -5 z^8 a^{-10} -5 z^8 a^{-12} +z^8 a^{-14} -5 z^7 a^{-9} -17 z^7 a^{-11} -12 z^7 a^{-13} -7 z^6 a^{-8} +6 z^6 a^{-10} +10 z^6 a^{-12} -3 z^6 a^{-14} +5 z^5 a^{-9} +30 z^5 a^{-11} +28 z^5 a^{-13} +3 z^5 a^{-15} +16 z^4 a^{-8} -z^4 a^{-10} -17 z^4 a^{-12} +2 z^4 a^{-14} +2 z^4 a^{-16} +3 z^3 a^{-9} -22 z^3 a^{-11} -33 z^3 a^{-13} -6 z^3 a^{-15} +2 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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