K12a300
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-13 q^6+19 q^5-23 q^4+24 q^3-22 q^2+18 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+37 t-49+37 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 155 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-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} -2 z^2 a^{-6} +z^2 a^{-8} -3 z^2+a^2+ a^{-2} -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} +8 z^9 a^{-3} +11 z^9 a^{-5} +7 z^9 a^{-7} -11 z^8 a^{-4} +7 z^8 a^{-8} +4 z^8+3 a z^7-3 z^7 a^{-1} -23 z^7 a^{-3} -37 z^7 a^{-5} -16 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-5 z^6 a^{-2} +z^6 a^{-4} -21 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} -6 z^6-8 a z^5-6 z^5 a^{-1} +29 z^5 a^{-3} +47 z^5 a^{-5} +10 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4+z^4 a^{-2} +14 z^4 a^{-4} +29 z^4 a^{-6} +14 z^4 a^{-8} -2 z^4 a^{-10} -3 z^4+6 a z^3+3 z^3 a^{-1} -17 z^3 a^{-3} -21 z^3 a^{-5} -3 z^3 a^{-7} +4 z^3 a^{-9} +3 a^2 z^2-7 z^2 a^{-4} -9 z^2 a^{-6} -4 z^2 a^{-8} +5 z^2-a z+3 z a^{-3} +3 z a^{-5} +z a^{-7} -a^2- a^{-2} -1 }[/math] |
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