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Please cite/link your sources, if possible. At some point in the next few days, I will:
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51 are the mitzvos that the Rambam enumerates as related to avodah zarah (idolatry) - the most of any one section of halachos in his Mishneh Torah.
Psalm 27 (לדוד ה אורי) is said during 51 days of the year, outside Israel, according to many Nusach Ashkenaz and Sefard.
It is said staring on 1 Ellul and continues until Shemini Atzeret. 29 days in Elul + 22 days during Tishrei = 51.