K12n427
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+6 q^8-11 q^7+15 q^6-18 q^5+19 q^4-16 q^3+13 q^2-8 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+14 t^2-23 t+27-23 t^{-1} +14 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+4 z^4+4 z^2+1 }[/math] |
| Determinant | 113 |
| 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} +7 z^2 a^{-4} -z^2 a^{-8} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +11 z^9 a^{-5} +6 z^9 a^{-7} +4 z^8 a^{-2} +7 z^8 a^{-4} +10 z^8 a^{-6} +7 z^8 a^{-8} +z^7 a^{-1} -13 z^7 a^{-3} -25 z^7 a^{-5} -7 z^7 a^{-7} +4 z^7 a^{-9} -14 z^6 a^{-2} -39 z^6 a^{-4} -36 z^6 a^{-6} -10 z^6 a^{-8} +z^6 a^{-10} -3 z^5 a^{-1} +2 z^5 a^{-3} +3 z^5 a^{-5} -z^5 a^{-7} +z^5 a^{-9} +15 z^4 a^{-2} +40 z^4 a^{-4} +26 z^4 a^{-6} +7 z^4 a^{-8} +6 z^4 a^{-10} +3 z^3 a^{-1} +10 z^3 a^{-3} +11 z^3 a^{-5} -z^3 a^{-7} -2 z^3 a^{-9} +3 z^3 a^{-11} -5 z^2 a^{-2} -13 z^2 a^{-4} -6 z^2 a^{-6} -z^2 a^{-8} -3 z^2 a^{-10} -z a^{-1} -3 z a^{-3} -4 z a^{-5} +z a^{-9} -z a^{-11} +2 a^{-4} - a^{-8} }[/math] |
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