K12a347
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+21 q^5-29 q^4+35 q^3-37 q^2+33 q-26+18 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-23 t^2+54 t-69+54 t^{-1} -23 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+z^4-2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+2 z^4 a^{-2} -z^4 a^{-6} +z^4-a^2 z^2-3 z^2 a^{-2} +2 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +18 z^{10} a^{-2} +11 z^{10} a^{-4} +7 z^{10}+7 a z^9+12 z^9 a^{-1} +23 z^9 a^{-3} +18 z^9 a^{-5} +4 a^2 z^8-37 z^8 a^{-2} -3 z^8 a^{-4} +18 z^8 a^{-6} -12 z^8+a^3 z^7-20 a z^7-54 z^7 a^{-1} -72 z^7 a^{-3} -27 z^7 a^{-5} +12 z^7 a^{-7} -13 a^2 z^6+9 z^6 a^{-2} -27 z^6 a^{-4} -26 z^6 a^{-6} +5 z^6 a^{-8} -8 z^6-3 a^3 z^5+17 a z^5+62 z^5 a^{-1} +68 z^5 a^{-3} +12 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+25 z^4 a^{-2} +27 z^4 a^{-4} +10 z^4 a^{-6} -3 z^4 a^{-8} +24 z^4+2 a^3 z^3-7 a z^3-29 z^3 a^{-1} -25 z^3 a^{-3} -3 z^3 a^{-5} +2 z^3 a^{-7} -5 a^2 z^2-20 z^2 a^{-2} -10 z^2 a^{-4} -z^2 a^{-6} -16 z^2+2 a z+6 z a^{-1} +4 z a^{-3} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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