K12a50
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+12 q-17+22 q^{-1} -23 q^{-2} +23 q^{-3} -18 q^{-4} +13 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-20 t^2+30 t-33+30 t^{-1} -20 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+8 z^4+6 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-4 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+6 a^4 z^2+a^2 z^2-3 z^2 a^{-2} +5 z^2-2 a^6+a^4+3 a^2- a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+6 a^5 z^9+12 a^3 z^9+11 a z^9+5 z^9 a^{-1} +7 a^6 z^8-18 a^2 z^8+3 z^8 a^{-2} -8 z^8+6 a^7 z^7-4 a^5 z^7-42 a^3 z^7-51 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-9 a^6 z^6-8 a^4 z^6+9 a^2 z^6-11 z^6 a^{-2} -6 z^6+a^9 z^5-10 a^7 z^5-5 a^5 z^5+58 a^3 z^5+76 a z^5+20 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+5 a^6 z^4+6 a^4 z^4+2 a^2 z^4+11 z^4 a^{-2} +16 z^4-2 a^9 z^3+8 a^7 z^3+7 a^5 z^3-38 a^3 z^3-51 a z^3-12 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-4 a^6 z^2-a^4 z^2+2 a^2 z^2-5 z^2 a^{-2} -7 z^2+a^9 z-4 a^7 z-3 a^5 z+10 a^3 z+13 a z+4 z a^{-1} -z a^{-3} +2 a^6+a^4-3 a^2+ a^{-2} }[/math] |
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