K12a1226
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+12 q-17+22 q^{-1} -22 q^{-2} +22 q^{-3} -18 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-18 t^2+26 t-29+26 t^{-1} -18 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+12 z^4+5 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+25 a^2 z^6-6 z^6-13 a^4 z^4+38 a^2 z^4-13 z^4-12 a^4 z^2+29 a^2 z^2-12 z^2-5 a^4+10 a^2-4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+10 a^2 z^{10}+4 z^{10}+8 a^5 z^9+4 a^3 z^9+4 z^9 a^{-1} +8 a^6 z^8-16 a^4 z^8-38 a^2 z^8+3 z^8 a^{-2} -11 z^8+6 a^7 z^7-20 a^5 z^7-25 a^3 z^7-11 a z^7-11 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-19 a^6 z^6+27 a^4 z^6+73 a^2 z^6-11 z^6 a^{-2} +13 z^6+a^9 z^5-13 a^7 z^5+23 a^5 z^5+48 a^3 z^5+19 a z^5+4 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+19 a^6 z^4-25 a^4 z^4-80 a^2 z^4+11 z^4 a^{-2} -20 z^4-2 a^9 z^3+10 a^7 z^3-6 a^5 z^3-41 a^3 z^3-24 a z^3+4 z^3 a^{-1} +5 z^3 a^{-3} -4 a^6 z^2+17 a^4 z^2+39 a^2 z^2-2 z^2 a^{-2} +16 z^2-3 a^7 z+2 a^5 z+12 a^3 z+9 a z-2 z a^{-3} -5 a^4-10 a^2-4 }[/math] |
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