Elliptic curves: statistics

The database currently contains 687,520 elliptic curves in 333,562 isogeny classes, over 402 number fields of degree 2 to 6. Elliptic curves defined over $\mathbb{Q}$ are contained in a separate database.

Distribution of degrees and conductor norms

		conductor norm
		1-100	101-1000	1001-10000	10001-50000	50001-100000	100001-150000	Total
degree	2	23729	73399	119282	213551	62267	25173	517401
		4.59%	14.19%	23.05%	41.27%	12.03%	4.87%	75.26%
	3	22357	16396	3898	1749			44400
		50.35%	36.93%	8.78%	3.94%			6.46%
	4	38388	49271	9156				96815
		39.65%	50.89%	9.46%				14.08%
	5	7728	7826					15554
		49.68%	50.32%					2.26%
	6	4517	8833					13350
		33.84%	66.16%					1.94%
	Total	96719	155725	132336	215300	62267	25173	687520
		14.07%	22.65%	19.25%	31.32%	9.06%	3.66%

Distribution of degrees and ranks

Only curves where the rank has been computed are shown.

		rank
		0	1	2	3	Total
degree	2	222896	260753	32091	113	515853
		43.21%	50.55%	6.22%	0.02%	75.52%
	3	22880	20383	757		44020
		51.98%	46.30%	1.72%		6.44%
	4	46849	46058	2116	8	95031
		49.30%	48.47%	2.23%	0.01%	13.91%
	5	7070	7691	335		15096
		46.83%	50.95%	2.22%		2.21%
	6	5583	7093	357		13033
		42.84%	54.42%	2.74%		1.91%
	Total	305278	341978	35656	121	683033
		44.69%	50.07%	5.22%	0.02%

Distribution of degrees and torsion structures

		torsion structure
		trivial	$C_{2}$	$C_{3}$	$C_{4}$	$C_{2} \times C_{2}$	$C_{5}$	$C_{6}$	$C_{7}$	$C_{8}$	$C_{2} \times C_{4}$	$C_{9}$	$C_{3} \times C_{3}$	$C_{10}$	$C_{11}$	$C_{12}$	$C_{2} \times C_{6}$	$C_{13}$	$C_{14}$	$C_{15}$	$C_{16}$	$C_{2} \times C_{8}$	$C_{4} \times C_{4}$	$C_{17}$	$C_{18}$	$C_{3} \times C_{6}$	$C_{19}$	$C_{20}$	$C_{2} \times C_{10}$	$C_{21}$	$C_{22}$	$C_{2} \times C_{12}$	$C_{25}$	$C_{27}$	$C_{2} \times C_{14}$	$C_{2} \times C_{16}$	$C_{2} \times C_{18}$	$C_{37}$	Total
degree	2	164889	242793	27554	25958	37129	2138	11624	235	673	3196	99	216	237	10	112	456	1	14	7		27	14		2	10			5			2							517401
		31.87%	46.93%	5.33%	5.02%	7.18%	0.41%	2.25%	0.05%	0.13%	0.62%	0.02%	0.04%	0.05%	0.00%	0.02%	0.09%	0.00%	0.00%	0.00%		0.01%	0.00%		0.00%	0.00%			0.00%			0.00%							75.26%
	3	10512	21608	1755	2309	4245	401	2187	97	276	536	48		151	3	33	201	1	7		3	15			4			1	4	1		1			1				44400
		23.68%	48.67%	3.95%	5.20%	9.56%	0.90%	4.93%	0.22%	0.62%	1.21%	0.11%		0.34%	0.01%	0.07%	0.45%	0.00%	0.02%		0.01%	0.03%			0.01%			0.00%	0.01%	0.00%		0.00%			0.00%				6.46%
	4	18891	51772	2219	4930	10545	828	4089	205	798	1341	79		447	23	58	455	2	40	15	5	44		1	8				17		2					1			96815
		19.51%	53.48%	2.29%	5.09%	10.89%	0.86%	4.22%	0.21%	0.82%	1.39%	0.08%		0.46%	0.02%	0.06%	0.47%	0.00%	0.04%	0.02%	0.01%	0.05%		0.00%	0.01%				0.02%		0.00%					0.00%			14.08%
	5	3738	8139	274	607	1624	173	409	65	135	151	4		143	7		51		17			6							9				1		1				15554
		24.03%	52.33%	1.76%	3.90%	10.44%	1.11%	2.63%	0.42%	0.87%	0.97%	0.03%		0.92%	0.05%		0.33%		0.11%			0.04%							0.06%				0.01%		0.01%				2.26%
	6	4089	6489	330	306	938	153	497	95	80	68	22		145	23	9	46	7	18			3			13		2		7	5				1	2		1	1	13350
		30.63%	48.61%	2.47%	2.29%	7.03%	1.15%	3.72%	0.71%	0.60%	0.51%	0.16%		1.09%	0.17%	0.07%	0.34%	0.05%	0.13%			0.02%			0.10%		0.01%		0.05%	0.04%				0.01%	0.01%		0.01%	0.01%	1.94%
	Total	202119	330801	32132	34110	54481	3693	18806	697	1962	5292	252	216	1123	66	212	1209	11	96	22	8	95	14	1	27	10	2	1	42	6	2	3	1	1	4	1	1	1	687520
		29.40%	48.12%	4.67%	4.96%	7.92%	0.54%	2.74%	0.10%	0.29%	0.77%	0.04%	0.03%	0.16%	0.01%	0.03%	0.18%	0.00%	0.01%	0.00%	0.00%	0.01%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.01%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%