K12a910
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-13 q^6+20 q^5-26 q^4+28 q^3-27 q^2+23 q-16+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-22 t^2+36 t-41+36 t^{-1} -22 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-8 z^4-3 z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-5 z^4 a^{-2} -10 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4-2 z^2 a^{-2} -9 z^2 a^{-4} +5 z^2 a^{-6} +3 z^2-3 a^{-4} +2 a^{-6} +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} +9 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} +6 z^9 a^{-7} -5 z^8 a^{-2} -27 z^8 a^{-4} -9 z^8 a^{-6} +5 z^8 a^{-8} +8 z^8+4 a z^7-18 z^7 a^{-1} -27 z^7 a^{-3} -22 z^7 a^{-5} -14 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-7 z^6 a^{-2} +37 z^6 a^{-4} +12 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -18 z^6-8 a z^5+10 z^5 a^{-1} +26 z^5 a^{-3} +33 z^5 a^{-5} +17 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+7 z^4 a^{-2} -30 z^4 a^{-4} -11 z^4 a^{-6} +9 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+3 a z^3-4 z^3 a^{-1} -9 z^3 a^{-3} -21 z^3 a^{-5} -14 z^3 a^{-7} +5 z^3 a^{-9} +a^2 z^2-2 z^2 a^{-2} +16 z^2 a^{-4} +6 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2 a^{-10} -6 z^2+z a^{-3} +5 z a^{-5} +4 z a^{-7} -3 a^{-4} -2 a^{-6} +2 }[/math] |
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