K12a21
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+11 q^{10}-18 q^9+25 q^8-30 q^7+31 q^6-28 q^5+22 q^4-14 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+21 t^2-45 t+57-45 t^{-1} +21 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -4 z^4 a^{-6} +z^4 a^{-10} +2 z^2 a^{-2} +z^2 a^{-4} -3 z^2 a^{-6} +3 z^2 a^{-8} + a^{-2} + a^{-4} -2 a^{-6} +2 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +8 z^{10} a^{-8} +5 z^{10} a^{-10} +5 z^9 a^{-5} +13 z^9 a^{-7} +18 z^9 a^{-9} +10 z^9 a^{-11} +5 z^8 a^{-4} +10 z^8 a^{-6} +5 z^8 a^{-8} +10 z^8 a^{-10} +10 z^8 a^{-12} +3 z^7 a^{-3} -2 z^7 a^{-5} -20 z^7 a^{-7} -34 z^7 a^{-9} -14 z^7 a^{-11} +5 z^7 a^{-13} +z^6 a^{-2} -9 z^6 a^{-4} -31 z^6 a^{-6} -40 z^6 a^{-8} -41 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -10 z^5 a^{-5} +8 z^5 a^{-9} -4 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +5 z^4 a^{-4} +30 z^4 a^{-6} +43 z^4 a^{-8} +33 z^4 a^{-10} +11 z^4 a^{-12} -z^4 a^{-14} +5 z^3 a^{-3} +11 z^3 a^{-5} +13 z^3 a^{-7} +13 z^3 a^{-9} +9 z^3 a^{-11} +3 z^3 a^{-13} +3 z^2 a^{-2} -2 z^2 a^{-4} -13 z^2 a^{-6} -16 z^2 a^{-8} -9 z^2 a^{-10} -z^2 a^{-12} -z a^{-3} -4 z a^{-5} -5 z a^{-7} -5 z a^{-9} -3 z a^{-11} - a^{-2} + a^{-4} +2 a^{-6} +2 a^{-8} + a^{-10} }[/math] |
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