K12a543
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-21 q^6+30 q^5-36 q^4+38 q^3-35 q^2+28 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+57 t-77+57 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4+1 }[/math] |
| Determinant | 239 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -2 z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-5 z^2 a^{-2} +6 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +15 z^{10} a^{-4} +8 z^{10} a^{-6} +10 z^9 a^{-1} +23 z^9 a^{-3} +26 z^9 a^{-5} +13 z^9 a^{-7} +3 z^8 a^{-2} -9 z^8 a^{-4} +7 z^8 a^{-6} +11 z^8 a^{-8} +8 z^8+4 a z^7-17 z^7 a^{-1} -61 z^7 a^{-3} -65 z^7 a^{-5} -20 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-31 z^6 a^{-2} -37 z^6 a^{-4} -45 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+12 z^5 a^{-1} +59 z^5 a^{-3} +51 z^5 a^{-5} +4 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+39 z^4 a^{-2} +52 z^4 a^{-4} +40 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +12 z^4+4 a z^3-7 z^3 a^{-1} -25 z^3 a^{-3} -16 z^3 a^{-5} +z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-20 z^2 a^{-2} -22 z^2 a^{-4} -12 z^2 a^{-6} -3 z^2 a^{-8} -6 z^2+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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