K12n175
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+3 q^9-4 q^8+4 q^7-3 q^6+q^5-2 q^3+4 q^2-3 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+4 t^2+5 t-11+5 t^{-1} +4 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+z^2+1 }[/math] |
| Determinant | 3 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +11 z^4 a^{-4} -7 z^4 a^{-6} -2 z^2 a^{-2} +10 z^2 a^{-4} -11 z^2 a^{-6} +4 z^2 a^{-8} + a^{-2} +3 a^{-4} -6 a^{-6} +4 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-3} +3 z^9 a^{-5} +4 z^9 a^{-7} +3 z^9 a^{-9} +3 z^8 a^{-2} +5 z^8 a^{-4} -2 z^8 a^{-6} -z^8 a^{-8} +3 z^8 a^{-10} +z^7 a^{-1} -9 z^7 a^{-3} -20 z^7 a^{-5} -25 z^7 a^{-7} -14 z^7 a^{-9} +z^7 a^{-11} -15 z^6 a^{-2} -31 z^6 a^{-4} -22 z^6 a^{-6} -20 z^6 a^{-8} -14 z^6 a^{-10} -4 z^5 a^{-1} +7 z^5 a^{-3} +32 z^5 a^{-5} +37 z^5 a^{-7} +12 z^5 a^{-9} -4 z^5 a^{-11} +19 z^4 a^{-2} +48 z^4 a^{-4} +54 z^4 a^{-6} +40 z^4 a^{-8} +15 z^4 a^{-10} +3 z^3 a^{-1} -3 z^3 a^{-3} -20 z^3 a^{-5} -17 z^3 a^{-7} +3 z^3 a^{-11} -7 z^2 a^{-2} -26 z^2 a^{-4} -36 z^2 a^{-6} -23 z^2 a^{-8} -6 z^2 a^{-10} +3 z a^{-3} +6 z a^{-5} +3 z a^{-7} -z a^{-9} -z a^{-11} - a^{-2} +3 a^{-4} +6 a^{-6} +4 a^{-8} + a^{-10} }[/math] |
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