K12a895
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-20 q^6+29 q^5-36 q^4+40 q^3-36 q^2+30 q-21+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-27 t^2+51 t-63+51 t^{-1} -27 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-7 z^4+z^2+1 }[/math] |
| Determinant | 243 |
| 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^6-7 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-5 z^2 a^{-2} -z^2 a^{-4} +3 z^2 a^{-6} +4 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +18 z^{10} a^{-4} +9 z^{10} a^{-6} +12 z^9 a^{-1} +20 z^9 a^{-3} +19 z^9 a^{-5} +11 z^9 a^{-7} -2 z^8 a^{-2} -26 z^8 a^{-4} -7 z^8 a^{-6} +8 z^8 a^{-8} +9 z^8+4 a z^7-20 z^7 a^{-1} -53 z^7 a^{-3} -52 z^7 a^{-5} -19 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-23 z^6 a^{-2} +4 z^6 a^{-4} -6 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -17 z^6-7 a z^5+11 z^5 a^{-1} +44 z^5 a^{-3} +46 z^5 a^{-5} +12 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+23 z^4 a^{-2} +4 z^4 a^{-4} +5 z^4 a^{-6} +7 z^4 a^{-8} -2 z^4 a^{-10} +13 z^4+4 a z^3-4 z^3 a^{-1} -16 z^3 a^{-3} -15 z^3 a^{-5} -2 z^3 a^{-7} +5 z^3 a^{-9} +a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-8} +z^2 a^{-10} -6 z^2-a z-z a^{-1} +z a^{-3} -z a^{-5} -3 z a^{-7} -z a^{-9} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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