The present invention relates to a Spinacia oleracea seed designated 51-341 RZ and 51-342 RZ, which exhibits a combination of traits including very late bolting, slow growing, a semi-erect plant habit, a small leaf blade size and resistance to downy mildew (P. farinosa f. sp. spinaciae) races Pfs1 to 15. The present invention also relates to a Spinacia oleracea plant produced by growing the 51-341 RZ or 51-342 RZ seed. The invention further relates to methods for producing the spinach cultivar, represented by spinach variety 51-341 RZ and 51-342 RZ.