How does BigInteger store its data?

With an int[]

From the source:

/**
 * The magnitude of this BigInteger, in <i>big-endian</i> order: the
 * zeroth element of this array is the most-significant int of the
 * magnitude.  The magnitude must be "minimal" in that the most-significant
 * int ({@code mag[0]}) must be non-zero.  This is necessary to
 * ensure that there is exactly one representation for each BigInteger
 * value.  Note that this implies that the BigInteger zero has a
 * zero-length mag array.
 */
final int[] mag;