show · intro all knowls · up · search:

Welcome to the LMFDB, the database of L-functions, modular forms, and related objects. Our goal is to describe this data in ways that faithfully exhibit the connections between these objects and prompt further exploration and discovery. We note the following features.

Knowls: Interspersed throughout the LMFDB are underlined words. These words represent knowls, which are bits of context free information. A knowl is identified by a word or phrase underlined with a dotted line. Clicking on a knowl brings up a box of text containing information about the object. Clicking on the knowl a second time will retract the box of text.


  • Browsing: One way to investigate information on the database is through browsing. For each type of object in the database, you can browse by distinguishing features. For example, to look for information about L-functions, you can browse by degree or underlying object.

  • Searching: Another way to investigate is through searching. You can search either by using a label to find a specific object or by specifying certain characteristics an object may have. For each of these types of searching, there is an example in grey text, and a description of possible inputs. Some fields may be left blank (or with grey text) in a search.

  • Interesting: Each section of the LMFDB contains a link to a curated list of objects that are notable or interesting in some way.

  • Random To view a randomly selected object from the database, click the "Random": link at the top of the left sidebar. To see what a typical object of a given type looks like, you can click a link to see a random object of the type. You can also select a random object that satisfies a set of selection criteria by clicking the "random object" button below the search area.

  • Learn more: Each section of the LMFDB contains a "Learn more about" box on the right hand side with links to additional information including details regarding the source, extent, and reliability of the data.

  • Breadcrumbs: On the top left of the header of a given page there is a description of your current path of navigation. Clicking on an item in the path will take you back to that page.

Properties: On the upper right hand side of a homepage for an object there is often a box containing specific properties of the object. This box can be closed and opened by clicking on the vertical arrow.

Related Objects: Often below the properties box in the upper right hand side of a homepage for an object is a box containing links to the homepages of directly related objects.

Downloading: You may download available data, for example moment polynomials of the zeta function. Some data is available to download within a page, while other data may be obtained through a link in the navigation bar.

Feedback: If you encounter any issues or problems while using the LMFDB, please click on Feedback in the upper right hand corner of the header to file a report.

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2020-10-09 21:13:30
Referred to by:
History: (expand/hide all) Differences (show/hide)