I'm cross-posting from StackOverflow because I didn't get any answers
Looking at the Tables of elliptic curves of a given rank documentation page and at Mazur's Theorem, a question pops out at me: Is there a way to query for elliptic curves which have a torsion subgroup that is one of the nontrivial products mentioned in Mazur's theorem?
For example, how do I specify the difference between $\mathbb{Z} / \mathbb{Z} 2 \times \mathbb{Z}/\mathbb{Z} 2$ from $\mathbb{Z}/\mathbb{Z} 4$ if the torsion parameter is an integer when querying the tables?
Really, the icing on the cake would be an interface to the LMFDB with filtering capabilities on all of the fields available on their website. Does anything satisfying my desires exist?