From Solomon Schechter, Aspects of Rabbinic Theology, chapter 12.
The Zachuth of the pious ancestry may generally be described as the זכות אבות (the Zachuth of the Fathers), but the term Fathers is largely limited in Rabbinic literature to the three patriarchs, Abraham, Isaac, and Jacob, God's covenant with whom is so often appealed to already in the Bible. The Rabbinic rule is, "They call not Fathers but the three (patriarchs), and they call not Mothers but four" (Sarah, Rebecca, Rachel, and Leah) . The last statement with regard to the Mothers suggests that there is such a thing as the זכות אמהות (the Zachuth of the Mothers). This is in conformity with the Rabbinic statement in reference to Lev. 26:42 regarding God's remembering his covenant with the patriarchs, that there is also such a thing as the covenant with the Mothers . In another place, they speak even distinctly of the Zachuth of the Mothers, "If thou seest the Zachuth of the Fathers and the Zachuth of the Mothers, that they are on the decline, then hope for the grace of God."  And it would even seem that they would invoke the Zachuth of the Mothers together with the Zachuth of the Fathers in their prayers on public fasts prescribed on the occasion of general distress  . . .
 Berachoth, 16b. See, however, D.E.Z., ch.1, where they speak of seven Fathers who entered into a covenant with God. In Sirach (heading to c.44), the expression Fathers is even more extensive.
 T.K., 112c.
 See Jer. Sanhedrin, 27d, and Lev.R., 36,6. Cf. commentaries, and see also Cant.R., 2,9.
 See Pseudo-Jonathan to Exod. 18:9 and Mechilta, 54a. In our liturgy, the invocation of the Zachuth of the mothers is very rare. A Piyut (hymn) by R. Gershom b. Judah, recited on the eve of the New Year, has a reference to the covenant of the Mothers.