Convert PDF to image with high resolution

I'm trying to use the command line program convert to take a PDF into an image (JPEG or PNG). Here is one of the PDFs that I'm trying to convert.

I want the program to trim off the excess white-space and return a high enough quality image that the superscripts can be read with ease.

This is my current best attempt. As you can see, the trimming works fine, I just need to sharpen up the resolution quite a bit. This is the command I'm using:

convert -trim 24.pdf -resize 500% -quality 100 -sharpen 0x1.0 24-11.jpg

I've tried to make the following conscious decisions:

• resize it larger (has no effect on the resolution)
• make the quality as high as possible
• use the -sharpen (I've tried a range of values)

Any suggestions please on getting the resolution of the image in the final PNG/JPEG higher would be greatly appreciated!

It appears that the following works:

convert           \
   -verbose       \
   -density 150   \
   -trim          \
    test.pdf      \
   -quality 100   \
   -flatten       \
   -sharpen 0x1.0 \
    24-18.jpg

It results in the left image. Compare this to the result of my original command (the image on the right):

(To really see and appreciate the differences between the two, right-click on each and select "Open Image in New Tab...".)

Also keep the following facts in mind:

• The worse, blurry image on the right has a file size of 1.941.702 Bytes (1.85 MByte). Its resolution is 3060x3960 pixels, using 16-bit RGB color space.
• The better, sharp image on the left has a file size of 337.879 Bytes (330 kByte). Its resolution is 758x996 pixels, using 8-bit Gray color space.

So, no need to resize; add the -density flag. The density value 150 is weird -- trying a range of values results in a worse looking image in both directions!