def METHOD_NAME(self, force_recomputation=False):
    """
    Return the list of Conway-Sloane genus symbols in increasing order of primes dividing 2*det.
    EXAMPLES::
        sage: Q = DiagonalQuadraticForm(ZZ, [1,2,3,4])
        sage: Q.CS_genus_symbol_list()
        [Genus symbol at 2:    [2^-2 4^1 8^1]_6, Genus symbol at 3:     1^3 3^-1]
    """
    # Try to use the cached list
    if not force_recomputation:
        try:
            return self.__CS_genus_symbol_list
        except AttributeError:
            pass
    # Otherwise recompute and cache the list
    list_of_CS_genus_symbols = []
    for p in prime_divisors(2 * self.det()):
        list_of_CS_genus_symbols.append(self.local_genus_symbol(p))
    self.__CS_genus_symbol_list = list_of_CS_genus_symbols
    return list_of_CS_genus_symbols