K12n139
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -3 q^7+6 q^6-8 q^5+11 q^4-11 q^3+11 q^2-9 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+11 t^2-12 t+11-12 t^{-1} +11 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -9 z^4 a^{-2} +14 z^4 a^{-4} -5 z^4 a^{-6} +z^4-12 z^2 a^{-2} +18 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +3 z^2-6 a^{-2} +9 a^{-4} -4 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +10 z^9 a^{-3} +7 z^9 a^{-5} -3 z^8 a^{-2} +5 z^8 a^{-4} +9 z^8 a^{-6} +z^8-15 z^7 a^{-1} -45 z^7 a^{-3} -26 z^7 a^{-5} +4 z^7 a^{-7} -19 z^6 a^{-2} -53 z^6 a^{-4} -39 z^6 a^{-6} -5 z^6+24 z^5 a^{-1} +57 z^5 a^{-3} +21 z^5 a^{-5} -12 z^5 a^{-7} +44 z^4 a^{-2} +84 z^4 a^{-4} +52 z^4 a^{-6} +3 z^4 a^{-8} +9 z^4-14 z^3 a^{-1} -24 z^3 a^{-3} -2 z^3 a^{-5} +8 z^3 a^{-7} -29 z^2 a^{-2} -47 z^2 a^{-4} -28 z^2 a^{-6} -3 z^2 a^{-8} -7 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} +2 z a^{-9} +6 a^{-2} +9 a^{-4} +4 a^{-6} +2 }[/math] |
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