K12a247
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+20 q^5-24 q^4+26 q^3-23 q^2+19 q-13+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+39 t-53+39 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 163 |
| 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+2 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} -3 z^2+a^2+2 a^{-2} + a^{-4} - a^{-6} -2 }[/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} +z^8 a^{-2} -9 z^8 a^{-4} +z^8 a^{-6} +7 z^8 a^{-8} +4 z^8+3 a z^7-z^7 a^{-1} -16 z^7 a^{-3} -30 z^7 a^{-5} -14 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-2 z^6 a^{-2} +5 z^6 a^{-4} -18 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -5 z^6-8 a z^5-11 z^5 a^{-1} +13 z^5 a^{-3} +32 z^5 a^{-5} +6 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4-10 z^4 a^{-2} -2 z^4 a^{-4} +21 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} -5 z^4+7 a z^3+10 z^3 a^{-1} -6 z^3 a^{-3} -12 z^3 a^{-5} +2 z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2+9 z^2 a^{-2} -7 z^2 a^{-6} -3 z^2 a^{-8} +8 z^2-2 a z-3 z a^{-1} -z a^{-7} -a^2-2 a^{-2} + a^{-4} + a^{-6} -2 }[/math] |
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