K12a416
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+18 q^5-25 q^4+31 q^3-33 q^2+30 q-24+17 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-25 t^2+44 t-51+44 t^{-1} -25 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+3 z^4+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +6 z^2 a^{-4} -2 z^2 a^{-6} +5 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +8 z^{10} a^{-4} +5 z^{10}+6 a z^9+12 z^9 a^{-1} +20 z^9 a^{-3} +14 z^9 a^{-5} +4 a^2 z^8-19 z^8 a^{-2} +z^8 a^{-4} +14 z^8 a^{-6} -2 z^8+a^3 z^7-14 a z^7-39 z^7 a^{-1} -58 z^7 a^{-3} -25 z^7 a^{-5} +9 z^7 a^{-7} -13 a^2 z^6-12 z^6 a^{-2} -31 z^6 a^{-4} -26 z^6 a^{-6} +4 z^6 a^{-8} -24 z^6-3 a^3 z^5+4 a z^5+27 z^5 a^{-1} +53 z^5 a^{-3} +20 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+28 z^4 a^{-2} +40 z^4 a^{-4} +23 z^4 a^{-6} -4 z^4 a^{-8} +29 z^4+3 a^3 z^3+6 a z^3-6 z^3 a^{-1} -20 z^3 a^{-3} -5 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-17 z^2 a^{-2} -19 z^2 a^{-4} -9 z^2 a^{-6} -12 z^2-a^3 z-2 a z+z a^{-1} +3 z a^{-3} -z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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