K12a124
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-3 q^2+7 q-12+18 q^{-1} -22 q^{-2} +24 q^{-3} -22 q^{-4} +18 q^{-5} -13 q^{-6} +7 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+36 t-47+36 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+z^4 a^4+z^2 a^4+a^4+z^6 a^2+z^4 a^2+z^2 a^2+a^2-2 z^4-3 z^2-1+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+7 a^4 z^{10}+3 a^2 z^{10}+6 a^7 z^9+10 a^5 z^9+8 a^3 z^9+4 a z^9+5 a^8 z^8-4 a^6 z^8-13 a^4 z^8+4 z^8+3 a^9 z^7-15 a^7 z^7-36 a^5 z^7-24 a^3 z^7-3 a z^7+3 z^7 a^{-1} +a^{10} z^6-12 a^8 z^6-6 a^6 z^6+9 a^4 z^6-5 a^2 z^6+z^6 a^{-2} -6 z^6-8 a^9 z^5+16 a^7 z^5+54 a^5 z^5+32 a^3 z^5-6 a z^5-8 z^5 a^{-1} -3 a^{10} z^4+8 a^8 z^4+15 a^6 z^4+4 a^4 z^4-3 z^4 a^{-2} -3 z^4+5 a^9 z^3-11 a^7 z^3-33 a^5 z^3-20 a^3 z^3+3 a z^3+6 z^3 a^{-1} +2 a^{10} z^2-4 a^8 z^2-10 a^6 z^2-4 a^4 z^2+2 a^2 z^2+3 z^2 a^{-2} +5 z^2-a^9 z+2 a^7 z+7 a^5 z+5 a^3 z-z a^{-1} +a^8+2 a^6+a^4-a^2- a^{-2} -1 }[/math] |
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