K12a680
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+11 q^7-19 q^6+26 q^5-30 q^4+32 q^3-28 q^2+22 q-14+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-24 t^2+40 t-47+40 t^{-1} -24 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-11 z^4 a^{-2} +z^4 a^{-4} +2 z^4 a^{-6} +4 z^4-12 z^2 a^{-2} +10 z^2 a^{-4} -z^2 a^{-6} +5 z^2-5 a^{-2} +7 a^{-4} -3 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +6 z^9 a^{-1} +10 z^9 a^{-3} +15 z^9 a^{-5} +11 z^9 a^{-7} -3 z^8 a^{-2} -19 z^8 a^{-4} -z^8 a^{-6} +10 z^8 a^{-8} +5 z^8+3 a z^7-10 z^7 a^{-1} -30 z^7 a^{-3} -40 z^7 a^{-5} -18 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-11 z^6 a^{-2} +z^6 a^{-4} -21 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -11 z^6-8 a z^5+3 z^5 a^{-1} +31 z^5 a^{-3} +31 z^5 a^{-5} +2 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4+26 z^4 a^{-2} +24 z^4 a^{-4} +19 z^4 a^{-6} +9 z^4 a^{-8} -z^4 a^{-10} +8 z^4+6 a z^3+5 z^3 a^{-1} -5 z^3 a^{-3} -5 z^3 a^{-5} +2 z^3 a^{-7} +3 z^3 a^{-9} +2 a^2 z^2-19 z^2 a^{-2} -21 z^2 a^{-4} -10 z^2 a^{-6} -z^2 a^{-8} -5 z^2-2 a z-4 z a^{-1} -3 z a^{-3} -3 z a^{-5} -z a^{-7} +z a^{-9} +5 a^{-2} +7 a^{-4} +3 a^{-6} +2 }[/math] |
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