K12a1261
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+8 q^7-15 q^6+22 q^5-29 q^4+31 q^3-29 q^2+25 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-23 t^2+40 t-47+40 t^{-1} -23 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-9 z^4-3 z^2+1 }[/math] |
| Determinant | 195 |
| 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} -11 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4-12 z^2 a^{-4} +6 z^2 a^{-6} +3 z^2+3 a^{-2} -6 a^{-4} +3 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +12 z^{10} a^{-4} +6 z^{10} a^{-6} +9 z^9 a^{-1} +12 z^9 a^{-3} +11 z^9 a^{-5} +8 z^9 a^{-7} -z^8 a^{-2} -23 z^8 a^{-4} -8 z^8 a^{-6} +6 z^8 a^{-8} +8 z^8+4 a z^7-15 z^7 a^{-1} -30 z^7 a^{-3} -35 z^7 a^{-5} -21 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-13 z^6 a^{-2} +23 z^6 a^{-4} +2 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -17 z^6-8 a z^5+6 z^5 a^{-1} +23 z^5 a^{-3} +44 z^5 a^{-5} +28 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+6 z^4 a^{-2} -21 z^4 a^{-4} +4 z^4 a^{-6} +14 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+4 a z^3-3 z^3 a^{-1} -9 z^3 a^{-3} -26 z^3 a^{-5} -21 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2+2 z^2 a^{-2} +18 z^2 a^{-4} +z^2 a^{-6} -7 z^2 a^{-8} +2 z^2 a^{-10} -5 z^2+3 z a^{-3} +9 z a^{-5} +6 z a^{-7} -3 a^{-2} -6 a^{-4} -3 a^{-6} +1 }[/math] |
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