K12a73
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-17 q^6+25 q^5-31 q^4+34 q^3-31 q^2+26 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-17 t^2+51 t-71+51 t^{-1} -17 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 211 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -z^4 a^{-2} -2 z^4 a^{-6} -2 z^4+a^2 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} - a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +13 z^{10} a^{-4} +6 z^{10} a^{-6} +10 z^9 a^{-1} +17 z^9 a^{-3} +15 z^9 a^{-5} +8 z^9 a^{-7} -3 z^8 a^{-2} -18 z^8 a^{-4} +7 z^8 a^{-8} +8 z^8+4 a z^7-19 z^7 a^{-1} -48 z^7 a^{-3} -39 z^7 a^{-5} -10 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-14 z^6 a^{-2} +z^6 a^{-4} -16 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+14 z^5 a^{-1} +50 z^5 a^{-3} +34 z^5 a^{-5} -3 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+16 z^4 a^{-2} +10 z^4 a^{-4} +14 z^4 a^{-6} +6 z^4 a^{-8} -2 z^4 a^{-10} +10 z^4+4 a z^3-9 z^3 a^{-1} -24 z^3 a^{-3} -10 z^3 a^{-5} +7 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-8 z^2 a^{-2} -5 z^2 a^{-4} -4 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -4 z^2+2 z a^{-1} +4 z a^{-3} -3 z a^{-7} -z a^{-9} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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