I was reading the paper of Prof.Franz Lemmermeyer titled "Pell-conics" which is here, in that the author writes in page 9 that one can define Tamagawa numbers as $ c_p = \begin{cases} 2 & \text{ if } p \mid \Delta, \\ 1 & \text{otherwise}. \end{cases}. $
Then he writes that Gauss-genus theory implies that $\prod c_p=2(\rm{Cl^+(k):Cl^+(k)^2})$ where $Cl^+(k)$ is the narrow class group of $k$, but I have referred to articles in the reference but can't find any such statement upto my sight. I know that one can write $\rm{Cl_{\large gen}}\cong \rm{Cl(k)/Cl(k)^2}$ where $\rm{Cl_{\large gen}}$ is the genus class group, I read the entire book of Reciprocity laws written by Prof.Franz Lemmermeyer but can't find any such notion.
After intensive search I found this one, even though Prof.Franz remarks that " latter is twice the genus class number ", he didn't point to any proof or reference pointing to that statement.
So I want any reference or proof of this statement
How can one say that product of Tamagawa numbers is equal to twice the Genus class numbers ? Is there any reference ?
Please answer this question as I dont have a proper access to materials neither know the current works.
Thanking you all.
Iyengar.