K12a827
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+9 q^3-12 q^2+14 q-14+14 q^{-1} -10 q^{-2} +8 q^{-3} -5 q^{-4} +2 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-13 t^2+21 t-23+21 t^{-1} -13 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+11 z^4+5 z^2+1 }[/math] |
| Determinant | 99 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +2 z^6-a^4 z^4+3 a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +8 z^4-3 a^4 z^2+2 a^2 z^2-2 z^2 a^{-2} -2 z^2 a^{-4} +10 z^2-2 a^4+a^2-3 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+6 a^2 z^{10}+4 z^{10}+a^5 z^9+7 a z^9+8 z^9 a^{-1} -12 a^4 z^8-27 a^2 z^8+11 z^8 a^{-2} -4 z^8-7 a^5 z^7-23 a^3 z^7-47 a z^7-20 z^7 a^{-1} +11 z^7 a^{-3} +24 a^4 z^6+30 a^2 z^6-29 z^6 a^{-2} +9 z^6 a^{-4} -32 z^6+18 a^5 z^5+60 a^3 z^5+71 a z^5+z^5 a^{-1} -22 z^5 a^{-3} +6 z^5 a^{-5} -18 a^4 z^4+3 a^2 z^4+20 z^4 a^{-2} -12 z^4 a^{-4} +3 z^4 a^{-6} +56 z^4-20 a^5 z^3-52 a^3 z^3-35 a z^3+11 z^3 a^{-1} +9 z^3 a^{-3} -4 z^3 a^{-5} +z^3 a^{-7} +5 a^4 z^2-9 a^2 z^2-11 z^2 a^{-2} +3 z^2 a^{-4} -28 z^2+8 a^5 z+15 a^3 z+7 a z-3 z a^{-1} -2 z a^{-3} +z a^{-5} -2 a^4-a^2+3 a^{-2} +5 }[/math] |
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