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Arithmetic Algebraic Geometry
Let p and q be distinct primes. The old part of J o (pq) is the abelian subvariety A + B of J o (pq) generated by the images of the two indicated degeneracy maps. Here, J o (N ) denotes the Jacobian Pic o (X o (N )) of the standard modular curve X o (N ), for each integer N ≥ 1. Also, we have written J o (p) 2 for the product J o (p) × J o (p), and have used analogous notation for J o (q) 2 . The definitions of α and β will be given below; see also  , §2a. The structure of A was determineddoi:10.1007/978-1-4612-0457-2_13 fatcat:jmmgpnecojfl5azzgvljppta3u