In 1945 Wiman [W] showed that certain elliptic curves $E$ over $\mathbf Q$ have rank\* at least 4. (It seems this was the highest known rank of an elliptic curve over $\mathbf Q$ until 1974, when Penney--Pomerance found a curve of [rank at least 6](https://web.math.pmf.unizg.hr/~duje/tors/rk6.html).) 


The method of his proof appears to be rather elementary, defining a map from $E(Q)$ to a certain abelian 2-group $A$ by using the $p$-valuations of the $x$-coordinate of a point $(x,y) \in E(\mathbf Q)$ for various primes $p$.


However, due to some combination of my inadequate German and Wiman's somewhat archaic mathematical style, I cannot decipher the exact definition of the group $A$ and the map $E(\mathbf Q) \rightarrow A$. So I ask



> 
> **Question:** What is the precise definition, in modern terms, of Wiman's group $A$ and map $E(\mathbf Q) \rightarrow A$? 
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[W] *Wiman, A.*, [**Über den Rang von Kurven**
$y^2=x(x+a)(x+b)$](http://dx.doi.org/10.1007/BF02551577), Acta Math. 76, 225-251 (1945). [ZBL0061.07109](https://zbmath.org/?q=an:0061.07109).


\*: A bit confusingly, "rank" is used in this paper to mean "minimal number of generators of $E(\mathbf Q)$" rather than "minimal number of generators of $E(\mathbf Q)/E(\mathbf Q)\_{\operatorname{tors}}$", so to get the "correct" rank one has to subtract 2 from each of the values reported by Wiman. 



Wiman's method for bounding the rank of an elliptic curve
I have not read all the details of the article, but most of what I see is just descent by the isogeny $[2]$. The map is the Kummer map $$E(\mathbb{Q})\to \mathbb{Q}^{\times}/\square \times \mathbb{Q}^{\times}/\square \times \mathbb{Q}^{\times}/\square$$ which sends $(x,y)$ to $(x-e\_1,x-e\_2,x-e\_3)$. In modern terms this is the connecting homomorphism $E(\mathbb{Q})\to H^1\bigl(\mathbb{Q}, E[2]\bigr)$. The kernel of the map is $2E(\mathbb{Q})$ and the image in each of the component lies in the group generated by the prime divisors of $\Delta$. Looking at valuations at those primes corresponds to studying the image of the local map $E(\mathbb{Q}\_p) \to \mathbb{Q}\_p^{\times}/\square\times\dots$. So the article actually studies the $2$-Selmer group. Similar to Selmer's work around the same time using $3$-descent. The idea to define Selmer groups and relate it to Galois cohomology only appears (if I am not mistaken) later in the work of Cassels, Lang, Tate, ...


