In the table in the readme , we find :

Code:

digits optimal B1 expected curves
N(B1,B2,D)
default poly
20 11e3 74
25 5e4 214
30 25e4 430
35 1e6 904
40 3e6 2350
45 11e6 4480
50 43e6 7553
55 11e7 17769
60 26e7 42017
65 85e7 69408
Table 1: optimal B1 and expected number of curves to find a
factor of D digits with GMP-ECM.

Why do the second derivatives change sign ?

Does this come from the mathematics or is it from the details of

the computer technology used to compute the estimates , such as

available RAM , cache sizes at various levels , disk access times ,

etc. ?