Class groups of quadratic imaginary fields

Data from extensive computations on class groups of quadratic imaginary fields is available below. It is organized by fundamental discriminant $d$, and divided into four groups based on congruences:

• $|d|\equiv 3\pmod 8$
• $|d|\equiv 7\pmod 8$
• $|d|\equiv 4\pmod {16}$
• $|d|\equiv 8\pmod {16}$

For each congruence class above, there are 4096 files, indexed from $k=0$ to $k=4095$. The $k$th file contains data for $k\cdot 2^{28} \leq |d| \lt (k+1)\cdot 2^{28}$.

File and data format

The $k$th file of data for $|d|\equiv r\pmod{m}$ has filename of the form cl{$r$}mod{$m$}.{$k$}.gz (for example, file $12$ for $|d|\equiv7\pmod8$ is cl7mod8.12.gz). Files range in size from 50 to 200 megabytes, and need to be uncompressed with gzip. After uncompressing, there is one line per discriminant, with discriminants in order of their absolute value. The discriminants and associated class group data may be extracted as follows, where for $i\ge1$ we define $d_i$ to be the $i$th discriminant of the file:

• Initialise $d_0=-k\cdot2^{28}-r$.
• For $i\ge1$, let the data in line $i$ of the file be

  $a$

  $b$

  $c_1\ c_2\ \ldots\ c_t$

• Then
  • $d_{i} = d_{i-1}-m\cdot a$,
  • $h(d_{i}) = b$,
  • the invariant factors for the class group are $[c_1, c_2,\ldots, c_t]$.
  In particular, $b=\prod_{j=1}^t c_j$.

For example, the first two lines of file cl4mod16.1 are

$0$	$12160$	$380\ 4\ 4\ 2$
$2$	$4392$	$2196\ 2$

so

• $d_0=-1\cdot2^{28}-4=-268435460$, and then
• $d_1=d_0-16\cdot0=-268435460$, with class number $12160$,
• $d_2=d_1-16\cdot2=-268435492$, with class number $4392$,

and so on.

File download

$|d| \equiv$
$k =$	integer from 0 to 4095