K12a604
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-21 q^6+29 q^5-34 q^4+36 q^3-32 q^2+25 q-16+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-20 t^2+53 t-71+53 t^{-1} -20 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-2 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-2 z^2 a^{-2} +5 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2+2 a^{-4} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +14 z^{10} a^{-4} +8 z^{10} a^{-6} +7 z^9 a^{-1} +17 z^9 a^{-3} +23 z^9 a^{-5} +13 z^9 a^{-7} -3 z^8 a^{-2} -15 z^8 a^{-4} +4 z^8 a^{-6} +11 z^8 a^{-8} +5 z^8+3 a z^7-11 z^7 a^{-1} -49 z^7 a^{-3} -61 z^7 a^{-5} -21 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-6 z^6 a^{-2} -15 z^6 a^{-4} -39 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -7 z^6-7 a z^5+9 z^5 a^{-1} +57 z^5 a^{-3} +53 z^5 a^{-5} +4 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+9 z^4 a^{-2} +30 z^4 a^{-4} +35 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} -z^4+5 a z^3-6 z^3 a^{-1} -29 z^3 a^{-3} -20 z^3 a^{-5} +z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2-4 z^2 a^{-2} -13 z^2 a^{-4} -11 z^2 a^{-6} -3 z^2 a^{-8} +4 z^2-a z+z a^{-1} +5 z a^{-3} +3 z a^{-5} -a^2+2 a^{-4} + a^{-6} -1 }[/math] |
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