K12a711
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+21 q-30+37 q^{-1} -38 q^{-2} +36 q^{-3} -29 q^{-4} +19 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+53 t-65+53 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4+z^2+1 }[/math] |
| Determinant | 243 |
| 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+6 a^4 z^4-8 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+7 a^4 z^2-7 a^2 z^2-z^2 a^{-2} +4 z^2-a^6+2 a^4-a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+10 a^4 z^{10}+19 a^2 z^{10}+9 z^{10}+15 a^5 z^9+25 a^3 z^9+20 a z^9+10 z^9 a^{-1} +14 a^6 z^8+3 a^4 z^8-28 a^2 z^8+5 z^8 a^{-2} -12 z^8+9 a^7 z^7-18 a^5 z^7-69 a^3 z^7-70 a z^7-27 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-20 a^6 z^6-39 a^4 z^6-18 a^2 z^6-13 z^6 a^{-2} -16 z^6+a^9 z^5-11 a^7 z^5+2 a^5 z^5+49 a^3 z^5+58 a z^5+21 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+15 a^6 z^4+40 a^4 z^4+35 a^2 z^4+10 z^4 a^{-2} +24 z^4-a^9 z^3+7 a^7 z^3+9 a^5 z^3-9 a^3 z^3-15 a z^3-4 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2-5 a^6 z^2-15 a^4 z^2-15 a^2 z^2-2 z^2 a^{-2} -8 z^2-2 a^7 z-3 a^5 z-a^3 z+a^6+2 a^4+a^2+1 }[/math] |
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