K12n759
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-13 q^6+17 q^5-18 q^4+18 q^3-15 q^2+10 q-5+2 q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -7 t^2+28 t-41+28 t^{-1} -7 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-7 z^4 }[/math] |
| Determinant | 111 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^{-2} -4 z^4 a^{-4} -z^4 a^{-6} -6 z^2 a^{-4} +3 z^2 a^{-6} +z^2 a^{-8} +2 z^2+ a^{-2} -3 a^{-4} +3 a^{-6} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +4 z^9 a^{-3} +9 z^9 a^{-5} +5 z^9 a^{-7} +3 z^8 a^{-2} +z^8 a^{-4} +4 z^8 a^{-6} +6 z^8 a^{-8} +z^7 a^{-1} -8 z^7 a^{-3} -20 z^7 a^{-5} -7 z^7 a^{-7} +4 z^7 a^{-9} -3 z^6 a^{-2} +z^6 a^{-4} -10 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} +3 z^5 a^{-1} +16 z^5 a^{-3} +23 z^5 a^{-5} -10 z^5 a^{-9} +5 z^4 a^{-2} -9 z^4 a^{-4} -4 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} +3 z^4-5 z^3 a^{-1} -12 z^3 a^{-3} -18 z^3 a^{-5} -5 z^3 a^{-7} +6 z^3 a^{-9} -z^2 a^{-2} +11 z^2 a^{-4} +7 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} -5 z^2+2 z a^{-1} +5 z a^{-3} +5 z a^{-5} +3 z a^{-7} +z a^{-9} - a^{-2} -3 a^{-4} -3 a^{-6} - a^{-8} +1 }[/math] |
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