K12n803
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+5 q^8-10 q^7+14 q^6-16 q^5+18 q^4-15 q^3+12 q^2-8 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+14 t^2-21 t+23-21 t^{-1} +14 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+4 z^4+6 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} +9 z^4 a^{-4} -2 z^4 a^{-6} -2 z^2 a^{-2} +8 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} - a^{-2} +3 a^{-4} + a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +10 z^9 a^{-5} +5 z^9 a^{-7} +4 z^8 a^{-2} +5 z^8 a^{-4} +6 z^8 a^{-6} +5 z^8 a^{-8} +z^7 a^{-1} -14 z^7 a^{-3} -25 z^7 a^{-5} -7 z^7 a^{-7} +3 z^7 a^{-9} -14 z^6 a^{-2} -33 z^6 a^{-4} -24 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} -3 z^5 a^{-1} +4 z^5 a^{-3} +11 z^5 a^{-5} +6 z^5 a^{-7} +2 z^5 a^{-9} +14 z^4 a^{-2} +36 z^4 a^{-4} +17 z^4 a^{-6} -z^4 a^{-8} +4 z^4 a^{-10} +3 z^3 a^{-1} +9 z^3 a^{-3} -12 z^3 a^{-7} -3 z^3 a^{-9} +3 z^3 a^{-11} -4 z^2 a^{-2} -15 z^2 a^{-4} -6 z^2 a^{-6} +4 z^2 a^{-8} -z^2 a^{-10} -z a^{-1} -2 z a^{-3} +6 z a^{-7} +3 z a^{-9} -2 z a^{-11} + a^{-2} +3 a^{-4} - a^{-6} -2 a^{-8} }[/math] |
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