The present invention relates to a Spinacia oleracea seed designated 51-710 RZ, which exhibits a combination of traits including medium-late bolting, a semi-erect to horizontal plant habit, a smooth to semi-savoy leaf surface and resistance to downy mildew (P. farinosa f. sp. spinaciae) races Pfs1 to Pfs15. The present invention also relates to a Spinacia oleracea plant produced by growing the 51-710 RZ seed. The invention further relates to methods for producing the spinach cultivar, represented by spinach variety 51-710 RZ.
