K12a1208
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+19 q^7-29 q^6+36 q^5-39 q^4+38 q^3-31 q^2+22 q-12+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-23 t^2+58 t-77+58 t^{-1} -23 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 247 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +2 z^4 a^{-4} +z^4 a^{-6} -z^4 a^{-8} -z^4+z^2 a^{-2} -z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +2 a^{-2} -2 a^{-4} +2 a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +13 z^{10} a^{-4} +22 z^{10} a^{-6} +9 z^{10} a^{-8} +20 z^9 a^{-3} +22 z^9 a^{-5} +10 z^9 a^{-7} +8 z^9 a^{-9} +19 z^8 a^{-2} -7 z^8 a^{-4} -52 z^8 a^{-6} -22 z^8 a^{-8} +4 z^8 a^{-10} +12 z^7 a^{-1} -30 z^7 a^{-3} -69 z^7 a^{-5} -52 z^7 a^{-7} -24 z^7 a^{-9} +z^7 a^{-11} -27 z^6 a^{-2} -21 z^6 a^{-4} +40 z^6 a^{-6} +17 z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-12 z^5 a^{-1} +12 z^5 a^{-3} +59 z^5 a^{-5} +62 z^5 a^{-7} +25 z^5 a^{-9} -3 z^5 a^{-11} +11 z^4 a^{-2} +14 z^4 a^{-4} -17 z^4 a^{-6} -7 z^4 a^{-8} +10 z^4 a^{-10} -3 z^4+2 z^3 a^{-1} -z^3 a^{-3} -20 z^3 a^{-5} -32 z^3 a^{-7} -13 z^3 a^{-9} +2 z^3 a^{-11} +z^2 a^{-2} +4 z^2 a^{-4} +7 z^2 a^{-6} +2 z^2 a^{-8} -2 z^2 a^{-10} +z a^{-3} +3 z a^{-5} +5 z a^{-7} +3 z a^{-9} -2 a^{-2} -2 a^{-4} -2 a^{-6} - a^{-8} }[/math] |
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