K12a652
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-12 q^6+18 q^5-23 q^4+24 q^3-23 q^2+19 q-13+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+37 t-47+37 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4-5 z^2+1 }[/math] |
| Determinant | 155 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2-2 a^{-2} + a^{-4} - a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +7 z^9 a^{-3} +7 z^9 a^{-5} +5 z^9 a^{-7} +3 z^8 a^{-2} -6 z^8 a^{-4} +z^8 a^{-6} +5 z^8 a^{-8} +5 z^8+3 a z^7-6 z^7 a^{-1} -11 z^7 a^{-3} -15 z^7 a^{-5} -10 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-14 z^6 a^{-2} +z^6 a^{-4} -10 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -10 z^6-7 a z^5-2 z^5 a^{-1} +13 z^5 a^{-5} +10 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+12 z^4 a^{-2} +11 z^4 a^{-6} +12 z^4 a^{-8} -3 z^4 a^{-10} +5 z^4+4 a z^3+2 z^3 a^{-1} +8 z^3 a^{-3} -4 z^3 a^{-5} -9 z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -5 z^2 a^{-6} -6 z^2 a^{-8} +2 z^2 a^{-10} -2 z^2-z a^{-1} -4 z a^{-3} +3 z a^{-7} -a^2+2 a^{-2} + a^{-4} + a^{-6} + a^{-8} +1 }[/math] |
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