K12a1284
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+5 q^3-9 q^2+13 q-17+19 q^{-1} -18 q^{-2} +16 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-15 t^2+24 t-27+24 t^{-1} -15 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-13 z^4-5 z^2+1 }[/math] |
| Determinant | 123 |
| 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} -6 z^6+4 a^4 z^4-8 a^2 z^4+5 z^4 a^{-2} -14 z^4+5 a^4 z^2-3 a^2 z^2+8 z^2 a^{-2} -15 z^2+a^4+2 a^2+4 a^{-2} -6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+2 z^{10} a^{-2} +6 z^{10}+8 a^3 z^9+7 a z^9+z^9 a^{-1} +2 z^9 a^{-3} +10 a^4 z^8-3 a^2 z^8-7 z^8 a^{-2} +z^8 a^{-4} -21 z^8+9 a^5 z^7-17 a^3 z^7-29 a z^7-13 z^7 a^{-1} -10 z^7 a^{-3} +6 a^6 z^6-20 a^4 z^6-8 a^2 z^6+6 z^6 a^{-2} -6 z^6 a^{-4} +30 z^6+3 a^7 z^5-14 a^5 z^5+17 a^3 z^5+33 a z^5+15 z^5 a^{-1} +16 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+18 a^4 z^4+4 a^2 z^4-4 z^4 a^{-2} +12 z^4 a^{-4} -37 z^4-2 a^7 z^3+10 a^5 z^3-14 a^3 z^3-22 a z^3-5 z^3 a^{-1} -9 z^3 a^{-3} -a^8 z^2+3 a^6 z^2-7 a^4 z^2-a^2 z^2+9 z^2 a^{-2} -8 z^2 a^{-4} +27 z^2+4 a^3 z+5 a z+3 z a^{-1} +2 z a^{-3} +a^4-2 a^2-4 a^{-2} -6 }[/math] |
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