K12n215
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+5 q^8-8 q^7+10 q^6-10 q^5+9 q^4-7 q^3+5 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+8 t^2-13 t+15-13 t^{-1} +8 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 61 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} +z^4 a^{-8} +3 z^2 a^{-2} -2 z^2 a^{-4} -2 z^2 a^{-6} +2 z^2 a^{-8} +2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +4 z^9 a^{-7} +2 z^9 a^{-9} +2 z^8 a^{-4} -z^8 a^{-6} -2 z^8 a^{-8} +z^8 a^{-10} +2 z^7 a^{-3} -5 z^7 a^{-5} -16 z^7 a^{-7} -9 z^7 a^{-9} +z^6 a^{-2} -3 z^6 a^{-4} -z^6 a^{-6} +z^6 a^{-8} -2 z^6 a^{-10} -6 z^5 a^{-3} +6 z^5 a^{-5} +30 z^5 a^{-7} +21 z^5 a^{-9} +3 z^5 a^{-11} -4 z^4 a^{-2} -5 z^4 a^{-4} +2 z^4 a^{-6} +6 z^4 a^{-8} +4 z^4 a^{-10} +z^4 a^{-12} +3 z^3 a^{-3} -9 z^3 a^{-5} -23 z^3 a^{-7} -17 z^3 a^{-9} -6 z^3 a^{-11} +5 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2 a^{-8} -2 z^2 a^{-10} -2 z^2 a^{-12} +z a^{-3} +3 z a^{-5} +6 z a^{-7} +6 z a^{-9} +2 z a^{-11} -2 a^{-2} - a^{-4} }[/math] |
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