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Mordell curves with rank lower bound ≥ 8

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showing 128 of 5563 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#62 [0, 0, 0, 0, -9088007366299…] ≥ 17 trivial 155.36 157.85 11.83 165.30
#308 [0, 0, 0, 0, 24537619889008…] ≥ 17 trivial 155.36 164.44 12.38 171.89
#5545 [0, 0, 1, 0, -4548387139104…] ≥ 17 trivial 156.02 184.09 14.02 191.55
#5546 [0, 0, 1, 0, 16845878292979…] ≥ 17 trivial 156.02 177.50 13.47 184.96
#5551 [0, 0, 1, 0, 47295953934055…] ≥ 17 trivial 156.07 165.75 12.49 173.21
#5552 [0, 0, 1, 0, -1276990756219…] ≥ 17 trivial 156.07 172.34 13.04 179.80
#5446 [0, 0, 0, 0, 23799778972095…] ≥ 17 trivial 157.09 173.59 13.14 181.04
#5448 [0, 0, 0, 0, -6425940322465…] ≥ 17 trivial 157.09 180.18 13.69 187.64
#5353 [0, 0, 1, 0, -3721250327597…] ≥ 17 trivial 162.09 169.88 12.84 177.33
#5355 [0, 0, 1, 0, 10047375884514…] ≥ 17 trivial 162.09 176.47 13.38 183.92
#5352 [0, 0, 1, 0, 38164268996399…] ≥ 17 trivial 168.83 169.93 12.84 177.38
#5354 [0, 0, 1, 0, -1030435262902…] ≥ 17 trivial 168.83 176.52 13.39 183.97
#46 [0, 0, 1, 0, -4894683839134…] ≥ 16 trivial 136.20 142.79 10.58 150.25
#64 [0, 0, 1, 0, 18128458663461…] ≥ 16 trivial 136.20 136.20 10.03 143.66
#68 [0, 0, 0, 0, 46974552981863…] ≥ 15 trivial 122.91 124.29 9.04 131.75
#305 [0, 0, 0, 0, -1268312930510…] ≥ 15 trivial 122.91 130.88 9.59 138.34
#5410 [0, 0, 1, 0, 33372439031705…] ≥ 15 trivial 158.78 169.66 12.82 177.11
#5411 [0, 0, 1, 0, -9010558538560…] ≥ 15 trivial 158.78 176.25 13.37 183.71
#4756 [0, 0, 1, 0, 12280460053296…] ≥ 14 trivial 103.19 103.19 7.28 110.64
#4757 [0, 0, 1, 0, -3315724214390…] ≥ 14 trivial 103.19 109.78 7.83 117.23
#4886 [0, 0, 1, 0, -1197774028283…] ≥ 14 trivial 142.92 153.79 11.50 161.25
#4959 [0, 0, 1, 0, 32339898763664…] ≥ 14 trivial 142.92 160.39 12.04 167.84
#639 [0, 0, 1, 0, 90519072625313…] ≥ 14 trivial 148.06 157.84 11.83 165.29
#4957 [0, 0, 1, 0, -2444014960883…] ≥ 14 trivial 148.06 164.43 12.38 171.89
#61 [0, 0, 1, 0, 75255852424198…] ≥ 13 trivial 87.29 88.39 6.04 95.85
#4952 [0, 0, 1, 0, -2031908015453…] ≥ 13 trivial 87.29 94.98 6.59 102.44
#5141 [0, 0, 0, 0, 19779840574906…] ≥ 13 trivial 91.06 94.93 6.59 102.39
#5162 [0, 0, 0, 0, -5340556955224…] ≥ 13 trivial 91.06 101.52 7.14 108.98
#4755 [0, 0, 0, 0, -1239793764346…] ≥ 13 trivial 91.22 94.00 6.51 101.45
#4921 [0, 0, 0, 0, 33474431637362…] ≥ 13 trivial 91.22 100.59 7.06 108.04
#5502 [0, 0, 0, 0, -3478138365920…] ≥ 13 trivial 120.04 142.11 10.52 149.57
#5503 [0, 0, 0, 0, 12881993947854…] ≥ 13 trivial 120.04 135.52 9.97 142.97
#4753 [0, 0, 0, 0, 41025014649039…] ≥ 12 trivial 80.09 82.57 5.56 90.03
#4923 [0, 0, 0, 0, -1107675395524…] ≥ 12 trivial 80.09 89.17 6.11 96.62
#4701 [0, 0, 1, 0, -1020920553852…] ≥ 12 trivial 83.30 84.40 5.71 91.85
#4702 [0, 0, 1, 0, 27564854954029…] ≥ 12 trivial 83.30 90.99 6.26 98.44
#4754 [0, 0, 0, 0, -2272988568342…] ≥ 12 trivial 84.61 86.00 5.85 93.45
#4924 [0, 0, 0, 0, 61370691345258…] ≥ 12 trivial 84.61 92.59 6.39 100.04
#4677 [0, 0, 0, 0, 25099601227316…] ≥ 12 trivial 88.32 90.80 6.25 98.26
#4953 [0, 0, 0, 0, -6776892331375…] ≥ 12 trivial 88.32 97.39 6.80 104.85
#4751 [0, 0, 0, 0, -9988201913147…] ≥ 11 trivial 72.66 75.14 4.94 82.60
#4926 [0, 0, 0, 0, 26968145165498…] ≥ 11 trivial 72.66 81.74 5.49 89.19
#4752 [0, 0, 0, 0, 12553604844459…] ≥ 11 trivial 74.21 75.60 4.98 83.06
#4927 [0, 0, 0, 0, -3389473308004…] ≥ 11 trivial 74.21 82.19 5.53 89.65
#4699 [0, 0, 0, 0, 35470887868736…] ≥ 11 trivial 76.58 82.28 5.54 89.74
#4817 [0, 0, 0, 0, -9577139724558…] ≥ 11 trivial 76.58 88.88 6.09 96.33
#5379 [0, 0, 1, 0, 39846666468086…] ≥ 11 trivial 77.10 82.52 5.56 89.97
#5412 [0, 0, 1, 0, -1075859994638…] ≥ 11 trivial 77.10 89.11 6.10 96.56
#5415 [0, 0, 0, 0, 16426738543362…] ≥ 11 trivial 78.07 85.35 5.79 92.80
#5418 [0, 0, 0, 0, -4435219406707…] ≥ 11 trivial 78.07 91.94 6.34 99.40
#4700 [0, 0, 0, 0, -4611148774373…] ≥ 11 trivial 80.04 82.81 5.58 90.26
#4816 [0, 0, 0, 0, 12450101690807…] ≥ 11 trivial 80.04 89.40 6.13 96.85
#3165 [0, 0, 1, 0, 44182596082121…] ≥ 11 ℤ/3ℤ 118.99 234.69 18.24 242.15
#4748 [0, 0, 1, 0, -1192930094217…] ≥ 11 trivial 118.99 241.28 18.79 248.74
#4749 [0, 0, 0, 0, 3612077876156] ≥ 10 trivial 61.13 63.90 4.00 71.35
#4928 [0, 0, 0, 0, -9752610265621…] ≥ 10 trivial 61.13 70.49 4.55 77.95
#4750 [0, 0, 0, 0, -5721469548799] ≥ 10 trivial 63.43 64.82 4.08 72.27
#4929 [0, 0, 0, 0, 15447967781757…] ≥ 10 trivial 63.43 71.41 4.63 78.87
#4693 [0, 0, 0, 0, -5673632565728…] ≥ 10 trivial 65.54 69.41 4.46 76.86
#4814 [0, 0, 0, 0, 15318807927467…] ≥ 10 trivial 65.54 76.00 5.01 83.45
#4691 [0, 0, 0, 0, 68513487607153] ≥ 10 trivial 67.30 69.78 4.49 77.24
#4815 [0, 0, 0, 0, -1849864165393…] ≥ 10 trivial 67.30 76.38 5.04 83.83
#5414 [0, 0, 1, 0, 72989388244528…] ≥ 10 trivial 67.73 79.12 5.27 86.58
#5416 [0, 0, 1, 0, -2703310675723…] ≥ 10 trivial 67.73 72.53 4.72 79.98
#5465 [0, 0, 0, 0, -7869883814381…] ≥ 10 trivial 68.68 70.06 4.52 77.52
#5464 [0, 0, 0, 0, -1215942493949…] ≥ 10 trivial 69.02 75.54 4.97 82.99
#5472 [0, 0, 1, 0, -7733905284046…] ≥ 10 trivial 71.41 74.63 4.90 82.09
#3107 [0, 0, 0, 0, 46927269375243…] ≥ 10 ℤ/3ℤ 82.21 161.13 12.11 168.59
#4747 [0, 0, 0, 0, -1267036273131…] ≥ 10 trivial 82.21 167.72 12.66 175.18
#5480 [0, 0, 1, 0, 14585801770] ≥ 9 trivial 51.78 52.88 3.09 60.33
#5482 [0, 0, 1, 0, -393816647797] ≥ 9 trivial 51.78 59.47 3.63 66.92
#4668 [0, 0, 0, 0, -44865147851] ≥ 9 trivial 52.64 55.12 3.27 62.58
#4950 [0, 0, 0, 0, 1211358991977] ≥ 9 trivial 52.64 61.71 3.82 69.17
#5496 [0, 0, 1, 0, -22548031687] ≥ 9 trivial 53.75 53.75 3.16 61.20
#5497 [0, 0, 1, 0, 608796855542] ≥ 9 trivial 53.75 60.34 3.71 67.79
#5500 [0, 0, 1, 0, -25185466405] ≥ 9 trivial 53.97 53.97 3.18 61.42
#5501 [0, 0, 1, 0, 680007592928] ≥ 9 trivial 53.97 60.56 3.73 68.01
#4684 [0, 0, 0, 0, 185418133372] ≥ 9 trivial 54.09 57.96 3.51 65.41
#4812 [0, 0, 0, 0, -5006289601044] ≥ 9 trivial 54.09 64.55 4.06 72.01
#5413 [0, 0, 0, 0, 19593731193566…] ≥ 9 trivial 56.96 76.49 5.05 83.95
#5417 [0, 0, 0, 0, -7256937479098…] ≥ 9 trivial 56.96 69.90 4.50 77.35
#4685 [0, 0, 0, 0, -463066403167] ≥ 9 trivial 57.31 59.79 3.66 67.25
#4813 [0, 0, 0, 0, 12502792885509] ≥ 9 trivial 57.31 66.38 4.21 73.84
#5470 [0, 0, 0, 0, 73325700650350…] ≥ 9 trivial 58.33 74.53 4.89 81.98
#5471 [0, 0, 0, 0, -1979793917559…] ≥ 9 trivial 58.33 81.12 5.44 88.57
#5468 [0, 0, 0, 0, -2961478305789…] ≥ 9 trivial 60.35 81.92 5.51 89.38
#5469 [0, 0, 0, 0, 79959914256319…] ≥ 9 trivial 60.35 88.51 6.06 95.97
#5361 [0, 0, 0, 0, 47700681504129] ≥ 9 trivial 65.48 69.06 4.43 76.52
#1643 [0, 0, 0, 0, 30457819633596…] ≥ 9 ℤ/3ℤ 69.17 137.24 10.12 144.70
#4746 [0, 0, 0, 0, -8223611301071…] ≥ 9 trivial 69.17 143.83 10.66 151.29
#3080 [0, 0, 1, 0, 87299817093221…] ≥ 9 ℤ/3ℤ 78.23 153.16 11.44 160.62
#5419 [0, 0, 1, 0, -2357095061516…] ≥ 9 trivial 78.23 159.75 11.99 167.21
#3081 [0, 0, 0, 0, 19988905798337…] ≥ 9 ℤ/3ℤ 88.37 177.84 13.50 185.30
#5420 [0, 0, 0, 0, -7403298443828…] ≥ 9 trivial 88.37 171.25 12.95 178.71
#5455 [0, 0, 1, 0, -163332357] ≥ 8 trivial 42.79 43.89 2.34 51.35
#5463 [0, 0, 1, 0, 4409973632] ≥ 8 trivial 42.79 50.48 2.89 57.94
#5459 [0, 0, 1, 0, -1133042644] ≥ 8 trivial 44.55 47.76 2.66 55.22
#5473 [0, 0, 1, 0, 30592151381] ≥ 8 trivial 44.55 54.36 3.21 61.81
#5377 [0, 0, 0, 0, 925219837] ≥ 8 trivial 44.87 47.36 2.63 54.81
#5398 [0, 0, 0, 0, -24980935599] ≥ 8 trivial 44.87 53.95 3.17 61.41
#5456 [0, 0, 1, 0, -469155968] ≥ 8 trivial 44.90 46.00 2.51 53.46
#5474 [0, 0, 1, 0, 12667211129] ≥ 8 trivial 44.90 52.59 3.06 60.05
#5444 [0, 0, 1, 0, 271151945] ≥ 8 trivial 44.90 44.90 2.42 52.36
#5466 [0, 0, 1, 0, -7321102522] ≥ 8 trivial 44.90 51.50 2.97 58.95
#5445 [0, 0, 1, 0, 331045189] ≥ 8 trivial 45.30 45.30 2.45 52.76
#5467 [0, 0, 1, 0, -8938220110] ≥ 8 trivial 45.30 51.90 3.00 59.35
#5462 [0, 0, 1, 0, -4014704591] ≥ 8 trivial 45.30 50.29 2.87 57.75
#4809 [0, 0, 0, 0, -2520963512] ≥ 8 trivial 45.49 49.36 2.79 56.82
#4810 [0, 0, 0, 0, 68066014824] ≥ 8 trivial 45.49 55.96 3.34 63.41
#5381 [0, 0, 0, 0, 1546290924] ≥ 8 trivial 45.61 48.39 2.71 55.84
#5392 [0, 0, 0, 0, -41749854948] ≥ 8 trivial 45.61 54.98 3.26 62.43
#5447 [0, 0, 1, 0, 440676412] ≥ 8 trivial 45.88 45.88 2.50 53.33
#4679 [0, 0, 0, 0, 1632201497] ≥ 8 trivial 46.01 48.49 2.72 55.95
#4811 [0, 0, 0, 0, -44069440419] ≥ 8 trivial 46.01 55.09 3.27 62.54
#5388 [0, 0, 0, 0, 2396616764] ≥ 8 trivial 46.49 49.26 2.78 56.72
#5407 [0, 0, 0, 0, -64708652628] ≥ 8 trivial 46.49 55.85 3.33 63.31
#5460 [0, 0, 1, 0, -1181122676] ≥ 8 trivial 46.75 47.85 2.67 55.30
#5457 [0, 0, 1, 0, 852863894] ≥ 8 trivial 47.20 47.20 2.61 54.65
#5391 [0, 0, 0, 0, 3120110801] ≥ 8 trivial 47.31 49.79 2.83 57.25
#5397 [0, 0, 0, 0, 3915127212] ≥ 8 trivial 47.47 50.24 2.87 57.70
#5458 [0, 0, 1, 0, 990890692] ≥ 8 trivial 47.50 47.50 2.64 54.95
#5394 [0, 0, 0, 0, 3653125129] ≥ 8 trivial 47.62 50.11 2.85 57.56
#5399 [0, 0, 0, 0, 4296777208] ≥ 8 trivial 47.66 50.43 2.88 57.89
#5401 [0, 0, 0, 0, 4860223021] ≥ 8 trivial 48.19 50.68 2.90 58.13
#4744 [0, 0, 0, 0, -5062143495128…] ≥ 8 trivial 59.45 119.84 8.67 127.29
#4862 [0, 0, 0, 0, 13667787436846…] ≥ 8 ℤ/3ℤ 59.45 126.43 9.21 133.88
#3064 [0, 0, 0, 0, 70829139273819…] ≥ 8 ℤ/3ℤ 59.60 115.90 8.34 123.36
#4745 [0, 0, 0, 0, -1912386760393…] ≥ 8 trivial 59.60 122.49 8.89 129.95