K12a526
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-17 q^6+25 q^5-31 q^4+34 q^3-31 q^2+26 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-25 t^2+43 t-51+43 t^{-1} -25 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 211 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -5 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-4 z^2 a^{-2} +2 z^2 a^{-6} +3 z^2- a^{-2} +2 a^{-4} - 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} +14 z^9 a^{-3} +13 z^9 a^{-5} +8 z^9 a^{-7} +3 z^8 a^{-2} -13 z^8 a^{-4} -z^8 a^{-6} +7 z^8 a^{-8} +8 z^8+4 a z^7-12 z^7 a^{-1} -28 z^7 a^{-3} -26 z^7 a^{-5} -10 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-23 z^6 a^{-2} -2 z^6 a^{-4} -10 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5-z^5 a^{-1} +11 z^5 a^{-3} +10 z^5 a^{-5} -3 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+19 z^4 a^{-2} +4 z^4 a^{-4} +6 z^4 a^{-6} +6 z^4 a^{-8} -2 z^4 a^{-10} +11 z^4+5 a z^3+5 z^3 a^{-1} +3 z^3 a^{-3} +6 z^3 a^{-5} +9 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-7 z^2 a^{-2} -2 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-10} -4 z^2-a z-2 z a^{-1} -2 z a^{-3} -4 z a^{-5} -4 z a^{-7} -z a^{-9} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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