K12a687
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-20 q^6+28 q^5-34 q^4+36 q^3-33 q^2+26 q-17+9 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+53 t-69+53 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4-4 z^2+1 }[/math] |
| Determinant | 223 |
| 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^2-6 z^2 a^{-2} +5 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -z^2+a^2-3 a^{-2} +3 a^{-4} -2 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +13 z^{10} a^{-4} +7 z^{10} a^{-6} +8 z^9 a^{-1} +17 z^9 a^{-3} +20 z^9 a^{-5} +11 z^9 a^{-7} +2 z^8 a^{-2} -7 z^8 a^{-4} +6 z^8 a^{-6} +9 z^8 a^{-8} +6 z^8+3 a z^7-13 z^7 a^{-1} -40 z^7 a^{-3} -45 z^7 a^{-5} -17 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-23 z^6 a^{-2} -31 z^6 a^{-4} -39 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -11 z^6-6 a z^5+11 z^5 a^{-1} +30 z^5 a^{-3} +26 z^5 a^{-5} +6 z^5 a^{-7} -7 z^5 a^{-9} -3 a^2 z^4+31 z^4 a^{-2} +41 z^4 a^{-4} +38 z^4 a^{-6} +15 z^4 a^{-8} -2 z^4 a^{-10} +8 z^4+3 a z^3-7 z^3 a^{-1} -7 z^3 a^{-3} -3 z^3 a^{-5} -2 z^3 a^{-7} +4 z^3 a^{-9} +3 a^2 z^2-18 z^2 a^{-2} -17 z^2 a^{-4} -15 z^2 a^{-6} -8 z^2 a^{-8} +z^2 a^{-10} -4 z^2+z a^{-1} -z a^{-9} -a^2+3 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} +1 }[/math] |
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