K12a1259
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+7 q^3-12 q^2+17 q-20+22 q^{-1} -21 q^{-2} +17 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-18 t^2+28 t-31+28 t^{-1} -18 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-10 z^4-4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -5 z^6+4 a^4 z^4-9 a^2 z^4+4 z^4 a^{-2} -9 z^4+5 a^4 z^2-7 a^2 z^2+5 z^2 a^{-2} -7 z^2+2 a^4-2 a^2+2 a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+4 z^{10} a^{-2} +10 z^{10}+10 a^3 z^9+7 a z^9+3 z^9 a^{-3} +11 a^4 z^8-6 a^2 z^8-16 z^8 a^{-2} +z^8 a^{-4} -34 z^8+9 a^5 z^7-21 a^3 z^7-37 a z^7-21 z^7 a^{-1} -14 z^7 a^{-3} +6 a^6 z^6-22 a^4 z^6-20 a^2 z^6+19 z^6 a^{-2} -5 z^6 a^{-4} +32 z^6+3 a^7 z^5-13 a^5 z^5+12 a^3 z^5+35 a z^5+28 z^5 a^{-1} +21 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+19 a^4 z^4+29 a^2 z^4-10 z^4 a^{-2} +8 z^4 a^{-4} -15 z^4-2 a^7 z^3+9 a^5 z^3-2 a^3 z^3-11 a z^3-9 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+3 a^6 z^2-9 a^4 z^2-15 a^2 z^2+6 z^2 a^{-2} -4 z^2 a^{-4} +8 z^2-2 a^5 z-a^3 z+a z+z a^{-1} +z a^{-3} +2 a^4+2 a^2-2 a^{-2} -1 }[/math] |
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