K12a440
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-8 q^9+13 q^8-19 q^7+22 q^6-23 q^5+21 q^4-16 q^3+12 q^2-6 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+20 t^2-28 t+31-28 t^{-1} +20 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +5 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -4 z^4 a^{-2} +10 z^4 a^{-4} +3 z^4 a^{-6} -3 z^4 a^{-8} -4 z^2 a^{-2} +12 z^2 a^{-4} -4 z^2 a^{-6} -z^2 a^{-8} - a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +4 z^{10} a^{-4} +10 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^9 a^{-3} +z^9 a^{-5} +5 z^9 a^{-7} +8 z^9 a^{-9} +3 z^8 a^{-2} -10 z^8 a^{-4} -34 z^8 a^{-6} -13 z^8 a^{-8} +8 z^8 a^{-10} +z^7 a^{-1} -12 z^7 a^{-3} -18 z^7 a^{-5} -27 z^7 a^{-7} -15 z^7 a^{-9} +7 z^7 a^{-11} -12 z^6 a^{-2} +43 z^6 a^{-6} +16 z^6 a^{-8} -11 z^6 a^{-10} +4 z^6 a^{-12} -4 z^5 a^{-1} +5 z^5 a^{-3} +22 z^5 a^{-5} +37 z^5 a^{-7} +12 z^5 a^{-9} -11 z^5 a^{-11} +z^5 a^{-13} +14 z^4 a^{-2} +13 z^4 a^{-4} -18 z^4 a^{-6} -10 z^4 a^{-8} +z^4 a^{-10} -6 z^4 a^{-12} +4 z^3 a^{-1} +4 z^3 a^{-3} -5 z^3 a^{-5} -12 z^3 a^{-7} -3 z^3 a^{-9} +3 z^3 a^{-11} -z^3 a^{-13} -7 z^2 a^{-2} -15 z^2 a^{-4} -5 z^2 a^{-6} +4 z^2 a^{-8} +2 z^2 a^{-10} +z^2 a^{-12} -z a^{-1} -2 z a^{-3} -4 z a^{-5} -3 z a^{-7} + a^{-2} +6 a^{-4} +5 a^{-6} + a^{-8} }[/math] |
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