K12a228
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-11 q^2+19 q-27+33 q^{-1} -35 q^{-2} +33 q^{-3} -26 q^{-4} +18 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+49 t-61+49 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-13 a^2 z^4-z^4 a^{-2} +6 z^4-2 a^6 z^2+11 a^4 z^2-15 a^2 z^2-z^2 a^{-2} +7 z^2-2 a^6+6 a^4-6 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+8 a^4 z^{10}+15 a^2 z^{10}+7 z^{10}+14 a^5 z^9+26 a^3 z^9+21 a z^9+9 z^9 a^{-1} +14 a^6 z^8+8 a^4 z^8-16 a^2 z^8+5 z^8 a^{-2} -5 z^8+9 a^7 z^7-21 a^5 z^7-77 a^3 z^7-73 a z^7-25 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-25 a^6 z^6-55 a^4 z^6-42 a^2 z^6-14 z^6 a^{-2} -30 z^6+a^9 z^5-12 a^7 z^5+10 a^5 z^5+71 a^3 z^5+69 a z^5+19 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+23 a^6 z^4+69 a^4 z^4+71 a^2 z^4+11 z^4 a^{-2} +40 z^4-a^9 z^3+6 a^7 z^3+3 a^5 z^3-24 a^3 z^3-25 a z^3-4 z^3 a^{-1} +z^3 a^{-3} -11 a^6 z^2-33 a^4 z^2-37 a^2 z^2-2 z^2 a^{-2} -17 z^2-2 a^7 z-2 a^5 z+2 a^3 z+2 a z+2 a^6+6 a^4+6 a^2+3 }[/math] |
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