Recently the elliptic curve $E:y^2+y=x^3-x^2$ of conductor $11$ (which appears in [my answer](https://mathoverflow.net/questions/11747/galoisian-sets-of-prime-numbers/32939#32939)) became my favourite elliptic over $\bf Q$ because the associated modular form
$$
F=q\prod\_{n>0}(1-q^n)^2(1-q^{11n})^2
$$
is such a nice "$\eta$-product". (This modular form is also associated to the isogenous elliptic curve
$y^2+y=x^3-x^2-10x-20$ which appears in [Franz's question](https://mathoverflow.net/questions/32964/quaternary-quadratic-forms-and-elliptic-curves-via-langlands).)


**Question.** Are there other elliptic curves over $\bf Q$ which have a simple minimal equation and whose associated modular form is a nice $\eta$-product or even a nice $\eta$-quotient?


I know two references which might have a bearing on the question


--- [Koike's article on McKay's conjecture](https://projecteuclid.org/journals/nagoya-mathematical-journal/volume-95/issue-none/On-McKays-conjecture/nmj/1118787564.full)


and


--- [p.18](https://books.google.com/books?id=MLdRYIg6pDkC&lpg=PR1&dq=ono%25252520web%25252520of%25252520modularity&pg=PA18#v=onepage&q&f=false) of Ono's *Web of modularity* on $\eta$-quotients.


Can someone provide a partial or exhaustive list of such nice pairs $(E,F)$ ?



Eta-products and modular elliptic curves
There is an exhaustive list in the paper [Y. Martin and K. Ono, Eta-Quotients and Elliptic
Curves, *Proc. Amer. Math Soc.* **125** (1997), no. 11, 3169--3176]. 
Suppose that $E\_N$ is an elliptic curve of conductor
$N$, then the corresponding $L$-series is assigned to the eta product
$$
\eta(a\tau)\eta(ab\tau)\eta(ac\tau)\eta(abc\tau),
$$
where $a+ab+ac+abc=24$, $a,b,c\in\mathbb Z$,
for the following values of $N$ and $(b,c)$:
$$ \begin{align\*}
 N &\quad (b,c)\cr
 11 &\quad (1,11)\cr
 14 &\quad (2,7)\cr
 15 &\quad (3,5)\cr
 20 &\quad (1,5)\cr
 24 &\quad (2,3)\cr
 27 &\quad (1,3)\cr
 32 &\quad (1,2)\cr
 36 &\quad (1,1)\cr
 \end{align\*}
$$
It is probably more exciting that all these elliptic curves and their $L$-series at $s=2$ appear in Boyd's conjectures on Mahler's measure. For a nice review of this story see
[M.D. Rogers, Hypergeometric formulas for lattice sums and Mahler measures, [arXiv:0806.3590](http://arxiv.org/abs/0806.3590)] and the original paper [D.W. Boyd, Mahler's measure and special values of $L$-functions, *Experiment. Math.* **7** (1998) 37--82].


