explicit example of computing ray class field for imaginary quadratic? Given an imaginary quadratic number field K, we can get its ray class field mod some ideal $\mathcal{m}$ by adjoining the j-invariant of an elliptic curve with complex multiplication given by $\mathcal{O}_K$ and the values of the Weber function at the non-zero $\mathcal{m}$-torsion of the curve. (See http://www.math.leidenuniv.nl/~psh/ANTproc/15cohenpsh.pdf)
I'm trying to get my hands on understanding this construction and explicit examples would be helpful- Does anyone know of a source that really explicitly goes through this computation of the ray class field for particular examples of K and choices of $\mathcal{m}$? 

You can do this directly for concrete examples using Sage or Magma, using Theorem 5.6 in Silverman's "Advanced topics...".
For instance, take $K=\mathbb{Q}(\sqrt{-7})$ and let us build the ray class field of conductor $3$. First, we need an elliptic curve $E$ with CM by $K$ (by $\mathcal{O}_K$). Here is one such curve:
$$E/\mathbb{Q}: y^2+xy=x^3-x^2-2x-1.$$ 
Since $j(E)\neq 0, 1728$, the $x$-coordinate function is a Weber function (see Cor. 5.7), and since $j(E)\in\mathbb{Q}$, we can build the ray class field of conductor $3$ by adjoining to $K$ the $x$-coordinates of all $3$ torsion points. For this, we can find the third division polynomial:
$$\psi_3:= 3x^4 - 3x^3 - 12x^2 - 12x - 1.$$
Let $L$ be the splitting field of $\psi_3$. Then, the ray class field of $K$ modulo $3$ is the field $H=KL$. (Note: the field $H$ turns out to be the extension $K(\alpha)$, where $\alpha$ is any root of $\psi_3$.)
You can do all this explicitly using Magma. The code is below:
E:=EllipticCurve([1,-1,0,-2,-1]);
HasComplexMultiplication(E);
P<x>:=PolynomialRing(Rationals());
f:=P!DivisionPolynomial(E,3);
f;
K:=NumberField(x^2+7);
F:=ext<K|f>;
H:=AbsoluteField(F);
H;

Above I computed $K(\alpha)$ where $\alpha$ is one $x$-coordinate of $3$ torsion. Let us calculate all the $x$-coordinates instead:
L:=SplittingField(f);
H2:=Compositum(K,L);
H2;
IsIsomorphic(H,H2);

Magma has ray class field functionality built in:
O:=MaximalOrder(K);
R:=RayClassField(3*O);
F3:=NumberField(R);
H3:=AbsoluteField(F3);
H3;
IsIsomorphic(H,H3);

