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Some method is proposed for finding Ein components in moduli spaces of stable rank 2 vector bundles with first Chern class c 1 = 0 on the projective 3-space. We formulate and illustrate a conjecture on the growth rate of the number of Ein components in dependence on the numbers of the second Chern class. We present a method for calculating the spectra of the above bundles, a recurrent formula, and an explicit formula for computing the number of the spectra of these bundles.

In this paper we suggest an implementation of elementary version of Runge's method for solving a family of diophantine equations of degree four. Moreover, the corresponding solving algorithm (in its optimized version) is implemented in the computer algebra system PARI/GP.

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