NDElkies

Member since 2026-06-03 02:28:50 UTC.

Curves (74)

curve	a-invariants	rank	torsion	log N	log \|Δ\|	Faltings height	naive height
#398	`[1, 0, 0, -1289259977445…, 56075504634839…]`	≥ 30	trivial	304.98	400.92	32.25	413.03
#399	`[1, 0, 0, -1122638888418…, 45019426548276…]`	≥ 29	trivial	306.00	401.75	32.27	412.61
#400	`[1, 0, 0, -2847874483810…, 58635720945607…]`	≥ 28	trivial	274.49	354.25	28.39	367.05
#403	`[1, 0, 0, -4789549597347…, 40388950701005…]`	≥ 28	trivial	313.99	375.75	30.22	389.33
#401	`[0, 0, 0, -9462421028937…, 35673551381852…]`	≥ 27	trivial	258.76	303.66	24.13	315.40
#402	`[1, -1, 1, -1272607077445…, 17471855868336…]`	≥ 27	trivial	247.24	335.00	26.94	350.82
#404	`[1, 0, 0, -1928799613292…, 98335186873093…]`	≥ 27	trivial	309.03	362.93	29.00	372.79
#477	`[0, 0, 1, -3096136477, 19662705790596]`	≥ 13	trivial	69.63	69.63	4.49	77.17
#475	`[0, 0, 1, -113679727, 682491235476]`	≥ 12	trivial	59.94	59.94	3.70	68.02
#556	`[0, 0, 1, -160923919, 872942963892]`	≥ 12	trivial	59.40	59.40	3.68	68.51
#476	`[0, 0, 1, -332557057, 2359264710636]`	≥ 12	trivial	59.19	59.19	3.74	70.50
#681	`[0, -1, 0, -226840098905, 45234150343722…]`	≥ 12	trivial	60.51	80.90	5.48	90.22
#1380	`[0, 1, 0, -1557588065548…, 17037557339777…]`	≥ 12	ℤ/2ℤ	70.25	122.19	8.89	130.37
#552	`[0, 0, 1, -13073767, -11170229244]`	≥ 11	trivial	52.84	52.84	3.10	60.77
#687	`[0, 0, 1, -36274357, 72401493396]`	≥ 11	trivial	51.31	55.03	3.31	63.83
#686	`[0, 0, 0, -127265047, 551353318330]`	≥ 11	trivial	51.28	54.74	3.44	67.60
#4058	`[1, 1, 0, 12360728041642, 29933108375647…]`	≥ 11	ℤ/2ℤ	64.57	96.03	6.69	103.21
#1381	`[0, -1, 0, -8468249023760…, 30310747685114…]`	≥ 11	ℤ/2ℤ	60.17	96.52	6.85	107.84
#1202	`[0, 1, 0, -4841195896937…, 12925635676335…]`	≥ 11	ℤ/2ℤ × ℤ/2ℤ	79.14	162.67	12.42	175.22
#4056	`[1, 1, 0, -129075833083, 95518746559857…]`	≥ 10	ℤ/2ℤ	55.14	80.57	5.41	88.36
#1382	`[0, -1, 0, -2166818128665, 12248052295665…]`	≥ 10	ℤ/2ℤ	51.06	84.00	5.87	96.83
#4158	`[0, -1, 0, -5488700773320…, -6047583648979…]`	≥ 10	ℤ/2ℤ × ℤ/2ℤ	57.56	126.54	9.24	134.15
#4157	`[1, -1, 0, -1765807184842…, 87258868579783…]`	≥ 10	ℤ/2ℤ × ℤ/2ℤ	59.94	127.49	9.39	137.66
#1203	`[1, 1, 1, -4872160096445…, -3100495634855…]`	≥ 10	ℤ/2ℤ × ℤ/2ℤ	60.88	132.43	9.75	140.70
#1395	`[1, 0, 0, -2128393013738…, 11958849002784…]`	≥ 10	ℤ/3ℤ	61.77	137.87	10.43	152.04
#4057	`[1, 1, 0, -4468681022, 10898822206752…]`	≥ 9	ℤ/2ℤ	44.42	68.53	4.46	78.27
#1383	`[0, -1, 0, -50722837785, 43932848419775…]`	≥ 9	ℤ/2ℤ	43.24	71.72	4.90	85.56
#3787	`[0, 1, 0, 35111895184806…, 17059676504171…]`	≥ 9	ℤ/3ℤ	55.88	108.47	7.72	115.91
#4161	`[0, -1, 0, -5358641471006…, 31524477168456…]`	≥ 9	ℤ/2ℤ × ℤ/2ℤ	52.47	112.77	8.09	120.27
#4160	`[0, 0, 0, -8302267538236…, 29100498651634…]`	≥ 9	ℤ/2ℤ × ℤ/2ℤ	51.87	107.33	7.88	121.58
#1647	`[1, -1, 1, -1371407722296…, 71308803097251…]`	≥ 9	ℤ/3ℤ	56.24	114.52	8.27	123.37
#3788	`[1, 0, 1, -1461285343169…, 21489517033413…]`	≥ 9	ℤ/3ℤ	52.23	115.85	8.60	130.18
#1204	`[1, 0, 1, -7540160955289…, 24800520566886…]`	≥ 9	ℤ/2ℤ × ℤ/2ℤ	53.16	124.19	9.14	135.11
#4159	`[1, -1, 0, -9995117836030…, 38378940454998…]`	≥ 9	ℤ/2ℤ × ℤ/2ℤ	51.19	123.05	9.13	135.95
#1643	`[0, 0, 0, 0, 30457819633596…]`	≥ 9	ℤ/3ℤ	69.17	137.24	10.12	144.70
#4163	`[1, -1, 0, -5152084861023, 44824110238869…]`	≥ 8	ℤ/2ℤ × ℤ/2ℤ	41.39	87.18	6.11	99.42
#1205	`[1, -1, 1, -5845120678571, 50144754265458…]`	≥ 8	ℤ/2ℤ × ℤ/2ℤ	41.08	90.45	6.28	99.80
#1654	`[1, 0, 1, -4714126488110…, 12457962738775…]`	≥ 8	ℤ/3ℤ	43.54	87.39	6.46	106.07
#4169	`[1, 1, 0, -29529355863, -4866824628470…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	38.21	76.42	5.06	83.94
#3786	`[1, -1, 0, -32988023466, 21769133846906…]`	≥ 7	ℤ/3ℤ	37.95	74.60	4.97	84.27
#4168	`[1, 1, 1, -41414392011, 31227585458588…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	37.44	74.89	5.00	84.95
#1661	`[1, 0, 1, -43204063985, 34565235981640…]`	≥ 7	ℤ/3ℤ	35.81	66.94	4.72	85.08
#4167	`[1, 1, 0, -49705570331, 40193474855597…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	35.98	75.86	5.07	85.50
#4166	`[1, -1, 0, -74933960103, -5780085605110…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	36.36	78.51	5.25	86.73
#1206	`[0, -1, 0, -78311948640, 73210350316245…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	34.91	78.01	5.23	86.87
#4165	`[1, 1, 0, -241641174856, 40112089591195…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	34.57	81.32	5.50	90.25
#4164	`[0, -1, 0, -1590129983521, 76173046741966…]`	≥ 7	ℤ/2ℤ × ℤ/2ℤ	34.59	84.79	5.87	95.90
#4150	`[0, -1, 0, -233824729, 1154819670169]`	≥ 6	ℤ/2ℤ × ℤ/2ℤ	30.38	60.75	3.78	69.42
#1668	`[1, -1, 0, -9026795691, 32997209797700…]`	≥ 6	ℤ/3ℤ	29.10	65.80	4.44	80.38
#4040	`[0, 1, 0, -895, 130929]`	≥ 5	ℤ/2ℤ	20.56	29.63	1.15	37.09
#4039	`[0, 1, 0, -4975, -101631]`	≥ 5	ℤ/2ℤ	20.46	28.90	1.12	37.15
#4038	`[1, 0, 1, -6613, -95028]`	≥ 5	ℤ/2ℤ	21.17	30.32	1.22	38.00
#4117	`[1, 1, 1, -174487014, 387295820946]`	≥ 5	ℤ/4ℤ	27.02	60.88	3.77	68.55
#4114	`[1, -1, 1, -174924457, 889700154456]`	≥ 5	ℤ/4ℤ	25.25	54.80	3.48	68.55
#426	`[0, 1, 1, -72, 210]`	≥ 4	trivial	13.12	13.12	-0.10	24.46
#4041	`[1, 1, 1, -449, -1330]`	≥ 4	ℤ/2ℤ	16.32	22.38	0.56	29.93
#3785	`[0, 0, 0, -22824, 1424529]`	≥ 4	ℤ/3ℤ	18.00	32.38	1.44	41.86
#4066	`[1, 0, 0, 1165886, 115195619]`	≥ 4	ℤ/4ℤ	20.66	46.12	2.53	53.52
#4068	`[1, 1, 1, -1879195, 978782432]`	≥ 4	ℤ/4ℤ	18.71	43.77	2.45	54.95
#4067	`[1, -1, 1, -2914381, 1907228661]`	≥ 4	ℤ/4ℤ	19.19	44.09	2.52	56.27
#4065	`[1, 0, 0, 1598846, 6881343029]`	≥ 4	ℤ/4ℤ	17.26	51.39	2.96	58.83
#4069	`[1, 1, 1, -12704813, 17424482906]`	≥ 4	ℤ/4ℤ	19.23	43.11	2.70	60.69
#4094	`[1, 1, 1, 1671, 254526]`	≥ 3	ℤ/4ℤ	14.50	30.97	1.26	38.41
#4091	`[1, -1, 1, 11479, -199848]`	≥ 3	ℤ/4ℤ	13.64	32.36	1.39	39.66
#4092	`[1, 0, 0, -14209, 749840]`	≥ 3	ℤ/4ℤ	14.57	31.73	1.37	40.58
#4093	`[1, 1, 1, -16065, 714870]`	≥ 3	ℤ/4ℤ	14.92	31.33	1.35	40.67
#804	`[1, -1, 0, -40608, 3106480]`	≥ 3	ℤ/2ℤ × ℤ/2ℤ	13.41	32.60	1.51	43.45
#1083	`[0, 1, 0, -25, 39]`	≥ 2	ℤ/2ℤ	6.99	11.15	-0.30	21.31
#424	`[0, 1, 1, 0, 0]`	≥ 1	trivial	3.76	3.76	-1.00	11.27
#425	`[1, -1, 1, 0, 0]`	≥ 1	trivial	3.97	3.97	-0.99	11.39
#658	`[0, 1, 1, -7, 5]`	≥ 1	ℤ/3ℤ	4.51	4.51	-0.74	17.59
#890	`[0, 0, 1, 0, -7]`	≥ 0	ℤ/3ℤ	3.30	9.89	-0.50	17.34
#879	`[1, -1, 1, -122, 1721]`	≥ 0	ℤ/12ℤ	4.50	20.84	0.42	28.39
#873	`[1, 0, 0, -1070, 7812]`	≥ 0	ℤ/2ℤ × ℤ/8ℤ	5.35	24.66	0.75	32.54

Contributions to other curves (2)

curve	a-invariants	contribution	rank	when
#730	`[0, -1, 0, -83998217835157960, 8463755759855448061507456]`	recorded the primes of bad reduction	15	2026-09-15 01:22:37 UTC
#617	`[0, 0, 0, -1243709484034594774252579512251439437046672200533376017, 548486337730283544420152286125150570880778768270835598547316636928034349688388249]`	recorded the primes of bad reduction	28	2026-09-09 03:55:54 UTC