Class number and class group problems for some non-normal totally real cubic number fields

Let {K-m}mgreater than or equal to4 be the family of non-normal totally real cubic number fields associated with the Q-irreducible cubic polynomials P-m (x) x(3)- mx(2) - (m + 1)X - 1, in greater than or equal to 4. We determine all these K-m's with class numbers h(m) less than or equal to 3: there are 14 such K-m's. Assuming the Generalized Riemann hypothesis for all the real quadratic number fields, we also prove that the exponents e(m) of the ideal class groups of these K,, go to infinity with m and we determine all these K-m's with ideal class groups of exponents e(m) less than or equal to 3: there are 6 such K-m's with ideal class groups of exponent 2, and 6 such K-m with ideal class groups Of exponent 3.