K12a682
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-9 q^6+13 q^5-16 q^4+16 q^3-15 q^2+12 q-8+5 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+25 t-29+25 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-5 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +2 z^4 a^{-2} +2 z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2+z^2 a^{-2} +z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -5 z^2+2 a^2+ a^{-2} - a^{-6} + a^{-8} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +2 z^9 a^{-1} +3 z^9 a^{-5} +5 z^9 a^{-7} -5 z^8 a^{-2} -18 z^8 a^{-4} -6 z^8 a^{-6} +5 z^8 a^{-8} +2 z^8+2 a z^7-2 z^7 a^{-1} -4 z^7 a^{-3} -20 z^7 a^{-5} -17 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6+11 z^6 a^{-2} +29 z^6 a^{-4} -3 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} -2 z^6-6 a z^5-2 z^5 a^{-1} +11 z^5 a^{-3} +36 z^5 a^{-5} +20 z^5 a^{-7} -9 z^5 a^{-9} -4 a^2 z^4-14 z^4 a^{-2} -15 z^4 a^{-4} +15 z^4 a^{-6} +16 z^4 a^{-8} -3 z^4 a^{-10} -7 z^4+4 a z^3-z^3 a^{-1} -7 z^3 a^{-3} -18 z^3 a^{-5} -12 z^3 a^{-7} +4 z^3 a^{-9} +5 a^2 z^2+5 z^2 a^{-2} +3 z^2 a^{-4} -7 z^2 a^{-6} -7 z^2 a^{-8} +z^2 a^{-10} +8 z^2+z a^{-1} +2 z a^{-5} +3 z a^{-7} -2 a^2- a^{-2} + a^{-6} + a^{-8} -2 }[/math] |
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