DATA.md

Obtaining the data

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The files `ec_curvedata_X.gp' were obtained from the LMFDB. We processed the files using the script 'write_aps()' found in generate-data.gp as follows

input filename	output filename	conductor range	bound for p
ec_curvedata_7500_10000.gp	first_example.data	7500-10000	$p\leq 100000 $
ec_curvedata_50000.gp	cond_50k_i.data for i=1,2,...,14	1-50000	$p\leq 50000$
ec_curvedata_200000.gp (first 5672 curves)	cond_200k_1.data	100002-100800	$p\leq 200000$

I generated some data from scratch for the following curves. This was done using the functions construct_box_curves(), construct_twists_sqrt_n1(), construct_twists_sqrt_n3(), construct_twists_sqrt_N() from the file generate-data.gp. If you want to do the same, you can try to use gp2c-run -g generate-data.gp and run the scripts from gp.

curve family	CM	filename	parameter range	bound for p
$y^2 = x^3 + Ax+b$		second_example.data	$(A,B)\in [-64,64]^2$	$p\leq 100000$
$y^2 = x^3 + Dx$	$\mathbb{Z}[i]$	sqrt_n1_D_10000_p_100000.data	$-10000\leq D\leq 10000$	$p\leq 100000$
$y^2 = x^3 + D$	$\mathbb{Z}[(1+\sqrt{-3})/2]$	sqrt_n3_D_10000_p_100000.data	$-10000\leq D\leq 10000$	$p\leq 100000$
$y^2 = x^3-270D^2x+1512D^3$	$\mathbb{Z}[\sqrt{-2}]$	sqrt_n2_D_10000-p_100000.data	$-10000\leq D\leq 10000$	$p\leq 100000$
$y^2 = x^3 - 35D^2x -98 D^3$	$\mathbb{Z}[(1+\sqrt{-7})/2]$	sqrt_n7_D_10000_p_100000.data	$-10000\leq D\leq 10000$	$p\leq 100000$