K12a1213
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+20 q^4-30 q^3+37 q^2-40 q+38-31 q^{-1} +22 q^{-2} -12 q^{-3} +5 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+31 t^2-51 t+61-51 t^{-1} +31 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6-z^4-3 z^2+1 }[/math] |
| Determinant | 253 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +3 z^6-2 a^2 z^4+z^4 a^{-2} -2 z^4 a^{-4} +2 z^4-4 z^2 a^{-2} +z^2 a^{-4} +a^2-3 a^{-2} +2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +23 z^{10} a^{-2} +10 z^{10} a^{-4} +13 z^{10}+20 a z^9+25 z^9 a^{-1} +15 z^9 a^{-3} +10 z^9 a^{-5} +19 a^2 z^8-50 z^8 a^{-2} -21 z^8 a^{-4} +5 z^8 a^{-6} -5 z^8+12 a^3 z^7-30 a z^7-82 z^7 a^{-1} -71 z^7 a^{-3} -30 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-27 a^2 z^6+17 z^6 a^{-2} +z^6 a^{-4} -14 z^6 a^{-6} -30 z^6+a^5 z^5-12 a^3 z^5+13 a z^5+78 z^5 a^{-1} +81 z^5 a^{-3} +27 z^5 a^{-5} -2 z^5 a^{-7} -3 a^4 z^4+11 a^2 z^4+25 z^4 a^{-2} +18 z^4 a^{-4} +9 z^4 a^{-6} +30 z^4+2 a^3 z^3-3 a z^3-31 z^3 a^{-1} -34 z^3 a^{-3} -8 z^3 a^{-5} -20 z^2 a^{-2} -11 z^2 a^{-4} -9 z^2+a z+5 z a^{-1} +4 z a^{-3} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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