K12a1263
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+17 q-25+31 q^{-1} -33 q^{-2} +32 q^{-3} -26 q^{-4} +18 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-21 t^2+49 t-63+49 t^{-1} -21 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 211 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-z^2 a^6-a^6+z^6 a^4+z^4 a^4+2 z^2 a^4+2 a^4+2 z^6 a^2+3 z^4 a^2-a^2+z^6+z^4+z^2+1-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+10 a^4 z^{10}+17 a^2 z^{10}+7 z^{10}+15 a^5 z^9+17 a^3 z^9+9 a z^9+7 z^9 a^{-1} +14 a^6 z^8-10 a^4 z^8-43 a^2 z^8+4 z^8 a^{-2} -15 z^8+9 a^7 z^7-29 a^5 z^7-63 a^3 z^7-47 a z^7-21 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-25 a^6 z^6-10 a^4 z^6+35 a^2 z^6-13 z^6 a^{-2} +3 z^6+a^9 z^5-12 a^7 z^5+25 a^5 z^5+75 a^3 z^5+59 a z^5+19 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+20 a^6 z^4+21 a^4 z^4-9 a^2 z^4+12 z^4 a^{-2} +6 z^4-a^9 z^3+5 a^7 z^3-9 a^5 z^3-40 a^3 z^3-35 a z^3-8 z^3 a^{-1} +2 z^3 a^{-3} -7 a^6 z^2-10 a^4 z^2-4 a^2 z^2-3 z^2 a^{-2} -4 z^2-a^7 z+2 a^5 z+8 a^3 z+7 a z+2 z a^{-1} +a^6+2 a^4+a^2+1 }[/math] |
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