Elliptic curves: statistics

The database currently contains 661,079 elliptic curves in 320,449 isogeny classes, over 396 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	23420	68607	100917	210673	62267	25173	491057
		4.77%	13.97%	20.55%	42.90%	12.68%	5.13%	74.28%
	3	22357	16396	3898	1749			44400
		50.35%	36.93%	8.78%	3.94%			6.72%
	4	38388	49271	9156				96815
		39.65%	50.89%	9.46%				14.64%
	5	7728	7826					15554
		49.68%	50.32%					2.35%
	6	4510	8743					13253
		34.03%	65.97%					2.00%
	Total	96403	150843	113971	212422	62267	25173	661079
		14.58%	22.82%	17.24%	32.13%	9.42%	3.81%

Distribution of degrees and ranks

Only curves where the rank has been computed are shown.

		rank
		0	1	2	3	Total
degree	2	211581	247980	30325	98	489984
		43.18%	50.61%	6.19%	0.02%	74.57%
	3	22880	20383	757		44020
		51.98%	46.30%	1.72%		6.70%
	4	46849	46058	2116	8	95031
		49.30%	48.47%	2.23%	0.01%	14.46%
	5	7070	7691	335		15096
		46.83%	50.95%	2.22%		2.30%
	6	5553	7033	357		12943
		42.90%	54.34%	2.76%		1.97%
	Total	293933	329145	33890	106	657074
		44.73%	50.09%	5.16%	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	156146	230951	26252	24600	35053	2021	11008	228	636	3007	94	216	227	10	107	419	1	14	7		27	14		2	10			5			2							491057
		31.80%	47.03%	5.35%	5.01%	7.14%	0.41%	2.24%	0.05%	0.13%	0.61%	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%							74.28%
	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%				6.72%
	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%			14.64%
	5	3740	8140	272	607	1624	173	408	65	135	151	4		143	7		51		17			6							9				1		1				15554
		24.05%	52.33%	1.75%	3.90%	10.44%	1.11%	2.62%	0.42%	0.87%	0.97%	0.03%		0.92%	0.05%		0.33%		0.11%			0.04%							0.06%				0.01%		0.01%				2.35%
	6	4049	6455	326	302	930	153	495	95	78	66	21		145	23	9	46	7	18			3			13		2		7	5				1	2		1	1	13253
		30.55%	48.71%	2.46%	2.28%	7.02%	1.15%	3.74%	0.72%	0.59%	0.50%	0.16%		1.09%	0.17%	0.07%	0.35%	0.05%	0.14%			0.02%			0.10%		0.02%		0.05%	0.04%				0.01%	0.02%		0.01%	0.01%	2.00%
	Total	193338	318926	30824	32748	52397	3576	18187	690	1923	5101	246	216	1113	66	207	1172	11	96	22	8	95	14	1	27	10	2	1	42	6	2	3	1	1	4	1	1	1	661079
		29.25%	48.24%	4.66%	4.95%	7.93%	0.54%	2.75%	0.10%	0.29%	0.77%	0.04%	0.03%	0.17%	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%