K12a31
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-11 q^6+16 q^5-20 q^4+22 q^3-20 q^2+17 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+33 t-43+33 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +2 z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2+4 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -3 z^2+a^2+3 a^{-4} -3 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +4 z^9 a^{-1} +7 z^9 a^{-3} +9 z^9 a^{-5} +6 z^9 a^{-7} -2 z^8 a^{-2} -18 z^8 a^{-4} -7 z^8 a^{-6} +5 z^8 a^{-8} +4 z^8+3 a z^7-4 z^7 a^{-1} -26 z^7 a^{-3} -41 z^7 a^{-5} -19 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6+18 z^6 a^{-4} -5 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -6 z^6-8 a z^5-4 z^5 a^{-1} +42 z^5 a^{-3} +68 z^5 a^{-5} +21 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4-5 z^4 a^{-2} +4 z^4 a^{-4} +23 z^4 a^{-6} +12 z^4 a^{-8} -3 z^4 a^{-10} -4 z^4+6 a z^3-31 z^3 a^{-3} -39 z^3 a^{-5} -9 z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2+z^2 a^{-2} -10 z^2 a^{-4} -14 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} +6 z^2-a z+z a^{-1} +7 z a^{-3} +7 z a^{-5} +z a^{-7} -z a^{-9} -a^2+3 a^{-4} +3 a^{-6} + a^{-8} -1 }[/math] |
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