K12a939
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+20 q^5-23 q^4+25 q^3-23 q^2+18 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -10 t^2+40 t-59+40 t^{-1} -10 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-10 z^4 }[/math] |
| Determinant | 159 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -4 z^4 a^{-2} -4 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-4 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +z^2 a^{-8} +2 z^2-2 a^{-2} +2 a^{-6} - a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +11 z^{10} a^{-4} +5 z^{10} a^{-6} +8 z^9 a^{-1} +7 z^9 a^{-3} +5 z^9 a^{-5} +6 z^9 a^{-7} -15 z^8 a^{-2} -36 z^8 a^{-4} -9 z^8 a^{-6} +6 z^8 a^{-8} +6 z^8+3 a z^7-28 z^7 a^{-1} -43 z^7 a^{-3} -25 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+5 z^6 a^{-2} +51 z^6 a^{-4} +13 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -19 z^6-8 a z^5+36 z^5 a^{-1} +75 z^5 a^{-3} +42 z^5 a^{-5} +z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4+21 z^4 a^{-2} -25 z^4 a^{-4} -20 z^4 a^{-6} +3 z^4 a^{-8} -2 z^4 a^{-10} +18 z^4+2 a z^3-20 z^3 a^{-1} -42 z^3 a^{-3} -31 z^3 a^{-5} -5 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-14 z^2 a^{-2} +4 z^2 a^{-4} +8 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} -10 z^2+4 z a^{-1} +9 z a^{-3} +7 z a^{-5} +3 z a^{-7} +z a^{-9} +2 a^{-2} -2 a^{-6} - a^{-8} +2 }[/math] |
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