K12a1223
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+7 q^8-12 q^7+16 q^6-20 q^5+21 q^4-19 q^3+16 q^2-11 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-10 t^3+18 t^2-23 t+25-23 t^{-1} +18 t^{-2} -10 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-13 z^6-12 z^4-2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -8 z^8 a^{-4} +z^8 a^{-6} +6 z^6 a^{-2} -25 z^6 a^{-4} +6 z^6 a^{-6} +13 z^4 a^{-2} -38 z^4 a^{-4} +13 z^4 a^{-6} +13 z^2 a^{-2} -27 z^2 a^{-4} +12 z^2 a^{-6} +5 a^{-2} -7 a^{-4} +3 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +10 z^{10} a^{-4} +6 z^{10} a^{-6} +3 z^9 a^{-1} -z^9 a^{-3} +5 z^9 a^{-5} +9 z^9 a^{-7} -17 z^8 a^{-2} -40 z^8 a^{-4} -12 z^8 a^{-6} +10 z^8 a^{-8} +z^8-14 z^7 a^{-1} -19 z^7 a^{-3} -33 z^7 a^{-5} -19 z^7 a^{-7} +9 z^7 a^{-9} +23 z^6 a^{-2} +60 z^6 a^{-4} +8 z^6 a^{-6} -18 z^6 a^{-8} +6 z^6 a^{-10} -5 z^6+20 z^5 a^{-1} +31 z^5 a^{-3} +43 z^5 a^{-5} +15 z^5 a^{-7} -14 z^5 a^{-9} +3 z^5 a^{-11} -17 z^4 a^{-2} -58 z^4 a^{-4} -14 z^4 a^{-6} +12 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +8 z^4-9 z^3 a^{-1} -16 z^3 a^{-3} -29 z^3 a^{-5} -9 z^3 a^{-7} +11 z^3 a^{-9} -2 z^3 a^{-11} +14 z^2 a^{-2} +34 z^2 a^{-4} +10 z^2 a^{-6} -2 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} -4 z^2+z a^{-1} +5 z a^{-3} +7 z a^{-5} +z a^{-7} -2 z a^{-9} -5 a^{-2} -7 a^{-4} -3 a^{-6} }[/math] |
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