Odd quadratic orders and real $j$-invariants https://arxiv.org/abs/2407.16703 #mathNT #mathAG
Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field $K$. Let $Cl(O)$ be the group of proper $O$-ideals and $Cl(O)[2]$ the kernel of multiplication by $2$ in $Cl(O)$. We describe explicitly the group $Cl(O)[2]$. In particular, we prove that its order is $2^{s_D-1}$ where $s_D$ is the number of prime divisors of $D$.
QOTO: Question Others to Teach Ourselves An inclusive, Academic Freedom, instance All cultures welcome. Hate speech and harassment strictly forbidden.
