K12n649
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^8-6 q^7+9 q^6-12 q^5+13 q^4-12 q^3+11 q^2-7 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+11 t^2-14 t+15-14 t^{-1} +11 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+z^4+z^2+1 }[/math] |
| Determinant | 77 |
| 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} +8 z^4 a^{-4} -4 z^4 a^{-6} -z^2 a^{-2} +6 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} + a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +9 z^9 a^{-5} +4 z^9 a^{-7} +4 z^8 a^{-2} +2 z^8 a^{-4} +2 z^8 a^{-8} +z^7 a^{-1} -17 z^7 a^{-3} -32 z^7 a^{-5} -14 z^7 a^{-7} -15 z^6 a^{-2} -29 z^6 a^{-4} -20 z^6 a^{-6} -6 z^6 a^{-8} -3 z^5 a^{-1} +12 z^5 a^{-3} +29 z^5 a^{-5} +15 z^5 a^{-7} +z^5 a^{-9} +15 z^4 a^{-2} +35 z^4 a^{-4} +30 z^4 a^{-6} +10 z^4 a^{-8} +2 z^3 a^{-1} -2 z^3 a^{-3} -7 z^3 a^{-5} +3 z^3 a^{-9} -4 z^2 a^{-2} -14 z^2 a^{-4} -15 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} +z a^{-3} -z a^{-5} -4 z a^{-7} -2 z a^{-9} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
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