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Curves with torsion ℤ/8ℤ

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showing 103 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1904 [1, 1, 1, 69056025716937…, -3349218851893…] ≥ 6 ℤ/8ℤ 60.46 251.75 19.67 259.18
#1903 [1, 0, 0, -3165956472564…, 68556991377202…] ≥ 6 ℤ/8ℤ 63.48 268.72 21.41 284.47
#1119 [1, 0, 0, -7568281857154…, 25340184713335…] ≥ 6 ℤ/8ℤ 70.51 284.70 22.76 300.90
#1897 [1, 1, 1, -1816104564575…, 28237703990352…] ≥ 6 ℤ/8ℤ 70.63 286.88 22.66 296.62
#1093 [1, 0, 0, -3042411698115…, 20659864464489…] ≥ 5 ℤ/8ℤ 42.83 183.33 14.09 194.58
#1905 [1, 0, 0, -4805101014203…, 24445672521664…] ≥ 5 ℤ/8ℤ 46.06 188.02 14.37 195.92
#1906 [1, 0, 0, -5845759088452…, 16867868851606…] ≥ 5 ℤ/8ℤ 46.58 206.53 16.00 217.24
#2848 [1, 0, 0, -1764377661167…, 28525101373243…] ≥ 5 ℤ/8ℤ 47.10 196.01 15.45 213.64
#2843 [1, 0, 0, -1430848035864…, 20832355619626…] ≥ 5 ℤ/8ℤ 47.29 199.52 16.33 226.83
#3558 [0, 1, 0, -7604174052792…, 25510854768692…] ≥ 5 ℤ/8ℤ 47.41 189.77 14.76 204.21
#2859 [1, 0, 0, -3561865423528…, 81454964632284…] ≥ 5 ℤ/8ℤ 47.60 189.76 14.66 201.93
#3555 [1, 0, 0, -7574665229116…, 80315560772780…] ≥ 5 ℤ/8ℤ 48.24 197.37 15.36 211.11
#2855 [1, 0, 0, -6846036141864…, 23774371692488…] ≥ 5 ℤ/8ℤ 48.27 194.77 14.97 204.07
#2830 [1, 0, 0, -1300076965855…, 61515175157366…] ≥ 5 ℤ/8ℤ 49.07 224.18 17.42 233.60
#2844 [1, 0, 0, -1974386092932…, 40967354642616…] ≥ 5 ℤ/8ℤ 49.77 202.24 15.54 209.76
#3559 [1, 0, 0, 58683080088749…, 22370205554074…] ≥ 5 ℤ/8ℤ 50.22 196.96 15.10 203.95
#3599 [1, 0, 0, -1228100006739…, 42047486310654…] ≥ 5 ℤ/8ℤ 52.31 206.79 15.92 214.42
#2829 [0, 1, 0, -1184963457155…, 15613761915399…] ≥ 5 ℤ/8ℤ 53.95 214.30 16.70 226.26
#2853 [0, -1, 0, -9585953417354…, 36124436799102…] ≥ 5 ℤ/8ℤ 54.11 192.63 18.66 260.17
#2821 [1, 0, 0, -1543132514199…, 28075861328873…] ≥ 5 ℤ/8ℤ 54.67 218.80 16.95 227.43
#1641 [0, 1, 0, -9554917251286…, 11690998742798…] ≥ 4 ℤ/8ℤ 29.64 118.60 8.66 128.96
#3501 [0, 1, 0, 31878668493415…, 60861931528788…] ≥ 4 ℤ/8ℤ 32.75 143.24 10.62 150.69
#1634 [1, 0, 0, 79266660223230…, -4455325195026…] ≥ 4 ℤ/8ℤ 32.86 134.71 9.92 142.16
#1635 [0, -1, 0, -2850385850045…, 58267281793422…] ≥ 4 ℤ/8ℤ 32.92 133.99 10.00 146.00
#1637 [0, 1, 0, -1813850220761…, 31222620731368…] ≥ 4 ℤ/8ℤ 33.71 134.92 10.00 144.75
#1638 [1, 0, 0, -9500954634454…, -2437000575224…] ≥ 4 ℤ/8ℤ 33.78 141.53 10.50 149.62
#1639 [1, 0, 0, 41842969373341…, -8896829519920…] ≥ 4 ℤ/8ℤ 33.85 148.72 11.08 156.05
#1640 [1, 0, 0, -3009239193932…, 22502924037598…] ≥ 4 ℤ/8ℤ 33.97 130.43 9.60 139.48
#824 [0, 1, 0, -2581070092659…, 15826335543370…] ≥ 4 ℤ/8ℤ 33.98 141.07 10.58 152.61
#3496 [0, 1, 0, -4461231976639…, -6607133009379…] ≥ 4 ℤ/8ℤ 34.05 139.49 10.32 147.35
#3497 [1, 0, 0, -2341217931897…, 43551937130598…] ≥ 4 ℤ/8ℤ 34.21 131.89 9.90 145.41
#1633 [1, 0, 0, -4248358377856…, 99784651087032…] ≥ 4 ℤ/8ℤ 35.02 134.89 9.93 142.46
#1636 [1, 0, 0, -6953750170048…, 70514107295864…] ≥ 4 ℤ/8ℤ 35.28 141.84 10.74 155.59
#3500 [1, 1, 1, -1682284032443…, 99353826862693…] ≥ 4 ℤ/8ℤ 35.30 142.96 10.63 151.67
#3502 [1, 0, 0, -8052297267075…, 87925698099943…] ≥ 4 ℤ/8ℤ 35.56 141.00 10.73 156.03
#3515 [1, 0, 0, -3767367091724…, 28145244321397…] ≥ 4 ℤ/8ℤ 36.70 139.90 11.38 167.56
#1568 [1, 0, 0, 386484616276, 15576139467609…] ≥ 3 ℤ/8ℤ 20.32 85.54 5.81 92.70
#1569 [0, -1, 0, -76509865360, 27624835288496…] ≥ 3 ℤ/8ℤ 20.33 81.69 5.49 89.24
#1189 [1, 1, 1, -78912468240, 84900580189747…] ≥ 3 ℤ/8ℤ 20.47 74.82 5.08 86.89
#1570 [1, 0, 0, -6201963287019…, 18799140047120…] ≥ 3 ℤ/8ℤ 20.60 88.51 6.53 106.89
#1571 [0, -1, 0, -363502229200, 52306571790340…] ≥ 3 ℤ/8ℤ 20.64 83.53 5.66 91.47
#1572 [1, 1, 1, -2822453613583…, 57714693438030…] ≥ 3 ℤ/8ℤ 20.71 85.40 6.32 104.53
#1564 [1, 0, 0, -8170675396524, 18949896093734…] ≥ 3 ℤ/8ℤ 20.94 94.59 6.57 102.30
#1565 [1, 0, 0, 27802687624817…, -8455682165542…] ≥ 3 ℤ/8ℤ 21.27 104.14 7.37 111.39
#1566 [1, 0, 0, 2602183183726, 44437189837743…] ≥ 3 ℤ/8ℤ 21.61 92.07 6.35 99.40
#1567 [1, 0, 0, -181665167180, 37065322475812…] ≥ 3 ℤ/8ℤ 21.68 81.33 5.49 89.83
#3495 [1, 0, 0, -7642328316420, 81191278314943…] ≥ 3 ℤ/8ℤ 22.36 87.38 6.17 100.61
#3492 [1, 1, 1, -4657343949510, -6374934039081…] ≥ 3 ℤ/8ℤ 22.60 91.64 6.33 99.12
#3493 [1, 0, 0, -1197506177564, 78531780732197…] ≥ 3 ℤ/8ℤ 22.63 87.95 6.03 95.93
#3503 [1, 0, 0, -3904014999750…, 93889132962931…] ≥ 3 ℤ/8ℤ 23.12 76.81 7.15 119.32
#3499 [0, 1, 0, -1684290984532…, 26605644903745…] ≥ 3 ℤ/8ℤ 23.33 86.84 7.11 116.79
#3498 [1, 0, 0, -8296983493957…, 91987422370623…] ≥ 3 ℤ/8ℤ 24.32 85.04 6.94 114.67
#1183 [1, 0, 0, -7486924540000…, 55964705995855…] ≥ 3 ℤ/8ℤ 27.56 129.03 9.44 136.70
#825 [1, 0, 0, -2499216832188…, -2459370495879…] ≥ 3 ℤ/8ℤ 29.32 124.04 9.03 131.79
#826 [1, 0, 0, -5623284730528…, 16230546792232…] ≥ 3 ℤ/8ℤ 31.62 125.69 9.86 148.04
#1182 [1, 0, 0, -139676614, 635368533620] ≥ 2 ℤ/8ℤ 12.44 42.16 3.11 67.88
#1181 [1, 1, 1, -15141210, 22670813415] ≥ 2 ℤ/8ℤ 12.64 41.52 2.69 61.21
#1470 [1, 0, 0, 563011, 17346765810] ≥ 2 ℤ/8ℤ 13.13 53.22 3.11 60.68
#1471 [1, 1, 1, -72485224, 236624449385] ≥ 2 ℤ/8ℤ 13.40 53.55 3.32 65.91
#1188 [1, 0, 0, -1558900, 7217210000] ≥ 2 ℤ/8ℤ 13.43 51.46 2.97 58.92
#1472 [0, 1, 0, -19315920, 54017604468] ≥ 2 ℤ/8ℤ 13.71 55.04 3.28 62.95
#1466 [1, 0, 0, -43776600200, -3369355023960…] ≥ 2 ℤ/8ℤ 13.82 75.22 5.03 85.12
#1467 [1, 0, 0, 97060195, 1294328797650] ≥ 2 ℤ/8ℤ 14.10 61.92 3.84 69.30
#1468 [1, 0, 0, 135956646, 128109873780] ≥ 2 ℤ/8ℤ 14.41 60.39 3.72 67.80
#1469 [1, 0, 0, -1195742680, 15666350994752] ≥ 2 ℤ/8ℤ 14.77 63.39 4.08 74.32
#3385 [1, 0, 0, -278232714, 1786218031908] ≥ 2 ℤ/8ℤ 15.08 53.21 3.50 69.95
#3386 [1, 0, 0, -495343314, 4240373022468] ≥ 2 ℤ/8ℤ 15.71 57.63 3.73 71.68
#3371 [1, 0, 0, -101871594, 378135545508] ≥ 2 ℤ/8ℤ 15.76 57.03 3.51 66.93
#3399 [1, 1, 1, -150244560, 59718809265] ≥ 2 ℤ/8ℤ 16.06 60.64 3.74 68.10
#3400 [1, 0, 0, -125268546914, 17065181337340…] ≥ 2 ℤ/8ℤ 16.64 56.22 4.70 88.27
#1040 [1, 1, 1, -17714, 900047] ≥ 1 ℤ/8ℤ 6.87 23.67 1.07 40.96
#2722 [0, 1, 0, -24400, 1458548] ≥ 1 ℤ/8ℤ 7.43 26.84 1.22 41.92
#1180 [1, 0, 0, -1785, 194922] ≥ 1 ℤ/8ℤ 7.49 30.41 1.21 37.89
#2715 [1, 0, 0, -6864, 223488] ≥ 1 ℤ/8ℤ 7.59 27.62 1.08 38.16
#2725 [1, 1, 1, -53200, 4740785] ≥ 1 ℤ/8ℤ 7.77 32.73 1.55 44.28
#2719 [1, 0, 0, -11764, 95888] ≥ 1 ℤ/8ℤ 8.31 32.24 1.38 39.73
#3061 [0, 1, 0, -1815520, 940954100] ≥ 1 ℤ/8ℤ 8.31 35.86 2.18 54.85
#3331 [1, 1, 1, -5199564, 4561336557] ≥ 1 ℤ/8ℤ 8.48 36.46 2.38 58.01
#3054 [1, 0, 0, 83616, -29981952] ≥ 1 ℤ/8ℤ 8.70 40.59 2.06 47.96
#2852 [1, 0, 0, -487459, 130953890] ≥ 1 ℤ/8ℤ 8.74 31.94 1.85 50.90
#3050 [1, 0, 0, 46376, 5353040] ≥ 1 ℤ/8ℤ 8.97 37.47 1.81 44.51
#3332 [1, 0, 0, -681440, 216441600] ≥ 1 ℤ/8ℤ 9.51 35.72 2.01 51.91
#2849 [1, 1, 1, -43400, 3397385] ≥ 1 ℤ/8ℤ 9.84 32.89 1.53 43.65
#3058 [1, 0, 0, -269700, 54090000] ≥ 1 ℤ/8ℤ 10.58 36.78 1.92 49.14
#2582 [1, 0, 0, -49095400, 132402324032] ≥ 1 ℤ/8ℤ 11.32 43.76 2.95 64.74
#2583 [1, 0, 0, 10134040, 425388708672] ≥ 1 ℤ/8ℤ 11.32 59.62 3.65 67.08
#2577 [1, 0, 0, -173039570, 782524080900] ≥ 1 ℤ/8ℤ 12.43 59.47 3.69 68.52
#2578 [1, 0, 0, 1051010430, -3114221930910…] ≥ 1 ℤ/8ℤ 12.43 68.37 4.38 75.66
#2561 [1, 0, 0, -2178935510140, 12379828114648…] ≥ 1 ℤ/8ℤ 12.49 61.89 5.37 96.84
#2562 [1, 0, 0, -8184310140, 32654373350760…] ≥ 1 ℤ/8ℤ 12.49 71.47 4.68 80.36
#883 [1, 1, 1, 35, -28] ≥ 0 ℤ/8ℤ 2.71 15.07 -0.06 22.28
#895 [1, 0, 0, -39, 90] ≥ 0 ℤ/8ℤ 3.04 10.73 -0.27 22.61
#935 [1, 1, 1, -4, 5] ≥ 0 ℤ/8ℤ 3.74 9.69 -0.50 17.37
#941 [0, 1, 0, 16, 180] ≥ 0 ℤ/8ℤ 3.87 16.41 0.05 23.85
#986 [1, 0, 0, -34, 68] ≥ 0 ℤ/8ℤ 4.62 12.77 -0.19 22.19
#1010 [1, 0, 0, 210, 900] ≥ 0 ℤ/8ℤ 5.35 20.65 0.41 27.65
#1011 [1, 0, 0, -15070, 710612] ≥ 0 ℤ/8ℤ 5.35 25.52 1.10 40.47
#1018 [0, 1, 0, -14624, 669300] ≥ 0 ℤ/8ℤ 5.82 28.97 1.23 40.38
#1032 [1, 0, 0, -420, 3600] ≥ 0 ℤ/8ℤ 6.54 20.69 0.46 29.92
#1033 [1, 1, 1, -70244, 7127525] ≥ 0 ℤ/8ℤ 6.57 31.65 1.54 45.09
#1039 [1, 0, 0, -3700, 67232] ≥ 0 ℤ/8ℤ 6.84 27.87 1.04 36.26
#1041 [1, 1, 1, -4890, 129447] ≥ 0 ℤ/8ℤ 7.11 23.44 0.87 37.10
#1059 [1, 0, 0, -770, 168900] ≥ 0 ℤ/8ℤ 8.78 30.14 1.19 37.60