Elliptic Curve Rank Leaderboard

Quartic twists with rank lower bound ≥ 6

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showing 170 of 5563 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#4695 [0, 0, 0, 40259977438769…, 0] ≥ 14 ℤ/2ℤ 151.42 229.39 17.80 236.84
#4958 [0, 0, 0, -1610399097550…, 0] ≥ 14 ℤ/2ℤ 151.42 233.54 18.15 241.00
#51 [0, 0, 0, 90389647280869…, 0] ≥ 13 ℤ/2ℤ 123.00 183.46 13.98 190.91
#4955 [0, 0, 0, -3615585891234…, 0] ≥ 13 ℤ/2ℤ 123.00 187.62 14.32 195.07
#52 [0, 0, 0, -2827529113871…, 0] ≥ 13 ℤ/2ℤ 127.69 193.79 14.84 201.24
#4956 [0, 0, 0, 11310116455485…, 0] ≥ 13 ℤ/2ℤ 127.69 197.95 15.18 205.40
#4772 [0, 0, 0, -1525990877673…, 0] ≥ 13 ℤ/2ℤ 129.34 191.94 14.68 199.39
#4917 [0, 0, 0, 61039635106957…, 0] ≥ 13 ℤ/2ℤ 129.34 196.10 15.03 203.55
#4774 [0, 0, 0, -9392287284872…, 0] ≥ 13 ℤ/2ℤ 134.69 204.30 15.71 211.75
#4918 [0, 0, 0, 37569149139489…, 0] ≥ 13 ℤ/2ℤ 134.69 208.45 16.06 215.91
#4776 [0, 0, 0, -1934800633488…, 0] ≥ 13 ℤ/2ℤ 141.55 220.28 17.05 227.73
#4920 [0, 0, 0, 48370015837217…, 0] ≥ 13 ℤ/2ℤ 141.55 216.12 16.70 223.58
#4765 [0, 0, 0, 11367990971876…, 0] ≥ 12 ℤ/2ℤ 107.44 163.42 12.31 170.88
#4911 [0, 0, 0, -4547196388750…, 0] ≥ 12 ℤ/2ℤ 107.44 167.58 12.65 175.04
#4766 [0, 0, 0, 17899271873584…, 0] ≥ 12 ℤ/2ℤ 108.35 164.78 12.42 172.24
#4912 [0, 0, 0, -7159708749433…, 0] ≥ 12 ℤ/2ℤ 108.35 168.94 12.77 176.40
#4767 [0, 0, 0, 30352395699298…, 0] ≥ 12 ℤ/2ℤ 109.41 166.37 12.55 173.82
#4913 [0, 0, 0, -1214095827971…, 0] ≥ 12 ℤ/2ℤ 109.41 170.53 12.90 177.98
#4769 [0, 0, 0, -1645077324548…, 0] ≥ 12 ℤ/2ℤ 111.77 171.44 12.98 178.89
#4915 [0, 0, 0, 65803092981934…, 0] ≥ 12 ℤ/2ℤ 111.77 175.60 13.32 183.05
#4768 [0, 0, 0, 12922927050511…, 0] ≥ 12 ℤ/2ℤ 112.31 170.71 12.92 178.17
#4916 [0, 0, 0, -5169170820204…, 0] ≥ 12 ℤ/2ℤ 112.31 174.87 13.26 182.33
#4770 [0, 0, 0, 14705318209188…, 0] ≥ 12 ℤ/2ℤ 113.95 178.01 13.52 185.46
#4771 [0, 0, 0, -7567865077941…, 0] ≥ 12 ℤ/2ℤ 119.42 182.92 13.93 190.38
#4773 [0, 0, 0, 29084092124144…, 0] ≥ 12 ℤ/2ℤ 124.62 200.78 15.42 208.23
#4986 [0, 0, 0, 60490706024165…, 0] ≥ 11 ℤ/2ℤ 82.13 126.99 9.27 134.45
#4988 [0, 0, 0, -2419628240966…, 0] ≥ 11 ℤ/2ℤ 82.13 131.15 9.62 138.60
#5504 [0, 0, 0, -5251191093898…, 0] ≥ 11 ℤ/2ℤ 100.77 161.10 12.11 168.56
#5541 [0, 0, 0, 21004764375593…, 0] ≥ 11 ℤ/2ℤ 100.77 165.26 12.46 172.72
#4763 [0, 0, 0, -1033477836241…, 0] ≥ 10 ℤ/2ℤ 72.61 107.87 7.68 115.33
#4906 [0, 0, 0, 41339113449671…, 0] ≥ 10 ℤ/2ℤ 72.61 112.03 8.03 119.49
#5249 [0, 0, 0, -1613637266474…, 0] ≥ 10 ℤ/2ℤ 99.07 157.56 11.82 165.02
#5250 [0, 0, 0, 40340931661865…, 0] ≥ 10 ℤ/2ℤ 99.07 153.41 11.47 160.86
#4690 [0, 0, 0, -248621438602, 0] ≥ 9 ℤ/2ℤ 56.64 82.88 5.60 90.33
#4951 [0, 0, 0, 994485754408, 0] ≥ 9 ℤ/2ℤ 56.64 87.04 5.94 94.49
#4760 [0, 0, 0, -727465200962, 0] ≥ 9 ℤ/2ℤ 58.78 86.10 5.86 93.55
#4905 [0, 0, 0, 2909860803848, 0] ≥ 9 ℤ/2ℤ 58.78 90.26 6.21 97.71
#5089 [0, 0, 0, 17297623511731…, 0] ≥ 9 ℤ/2ℤ 73.99 123.23 8.96 130.69
#5090 [0, 0, 0, -4324405877932…, 0] ≥ 9 ℤ/2ℤ 73.99 119.08 8.61 126.53
#5338 [0, 0, 0, -6369312392920…, 0] ≥ 9 ℤ/2ℤ 78.65 120.24 8.71 127.69
#5339 [0, 0, 0, 25477249571682…, 0] ≥ 9 ℤ/2ℤ 78.65 124.40 9.06 131.85
#5334 [0, 0, 0, -3640698460440…, 0] ≥ 9 ℤ/2ℤ 78.92 125.47 9.15 132.92
#5335 [0, 0, 0, 14562793841760…, 0] ≥ 9 ℤ/2ℤ 78.92 129.63 9.49 137.08
#4764 [0, 0, 0, -1035658306822…, 0] ≥ 9 ℤ/2ℤ 81.04 135.51 9.98 142.97
#4909 [0, 0, 0, 25891457670573…, 0] ≥ 9 ℤ/2ℤ 81.04 131.35 9.64 138.81
#5532 [0, 0, 0, 15913951595784, 0] ≥ 8 ℤ/2ℤ 54.32 95.35 6.64 102.81
#5534 [0, 0, 0, -3978487898946, 0] ≥ 8 ℤ/2ℤ 54.32 91.19 6.29 98.65
#5533 [0, 0, 0, 15960909912948, 0] ≥ 8 ℤ/2ℤ 54.50 95.36 6.64 102.82
#5542 [0, 0, 0, -3990227478237, 0] ≥ 8 ℤ/2ℤ 54.50 91.20 6.29 98.66
#4759 [0, 0, 0, -141262310897, 0] ≥ 8 ℤ/2ℤ 54.81 81.18 5.45 88.64
#4904 [0, 0, 0, 565049243588, 0] ≥ 8 ℤ/2ℤ 54.81 85.34 5.80 92.79
#5281 [0, 0, 0, -157485012321, 0] ≥ 8 ℤ/2ℤ 55.03 81.51 5.48 88.96
#5282 [0, 0, 0, 629940049284, 0] ≥ 8 ℤ/2ℤ 55.03 85.67 5.83 93.12
#5340 [0, 0, 0, -1805710054225, 0] ≥ 8 ℤ/2ℤ 56.69 88.82 6.09 96.28
#5341 [0, 0, 0, 7222840216900, 0] ≥ 8 ℤ/2ℤ 56.69 92.98 6.44 100.44
#5349 [0, 0, 0, 257381680598, 0] ≥ 8 ℤ/2ℤ 56.71 82.98 5.60 90.44
#5350 [0, 0, 0, -1029526722392, 0] ≥ 8 ℤ/2ℤ 56.71 87.14 5.95 94.59
#5342 [0, 0, 0, 297690369198, 0] ≥ 8 ℤ/2ℤ 57.00 83.42 5.64 90.87
#5343 [0, 0, 0, -1190761476792, 0] ≥ 8 ℤ/2ℤ 57.00 87.58 5.99 95.03
#5307 [0, 0, 0, -1210309950049…, 0] ≥ 8 ℤ/2ℤ 58.74 94.53 6.57 101.99
#5308 [0, 0, 0, 3025774875123, 0] ≥ 8 ℤ/2ℤ 58.74 90.37 6.22 97.83
#4762 [0, 0, 0, -1475249346169…, 0] ≥ 8 ℤ/2ℤ 59.14 95.13 6.62 102.58
#4907 [0, 0, 0, 3688123365423, 0] ≥ 8 ℤ/2ℤ 59.14 90.97 6.27 98.42
#5297 [0, 0, 0, 5328710675343, 0] ≥ 8 ℤ/2ℤ 59.88 92.07 6.36 99.53
#5247 [0, 0, 0, 5643558023103, 0] ≥ 8 ℤ/2ℤ 59.99 92.24 6.38 99.70
#5248 [0, 0, 0, -2257423209241…, 0] ≥ 8 ℤ/2ℤ 59.99 96.40 6.72 103.86
#5086 [0, 0, 0, 52177525129606…, 0] ≥ 8 ℤ/2ℤ 68.47 105.82 7.51 113.28
#5087 [0, 0, 0, -1304438128240…, 0] ≥ 8 ℤ/2ℤ 68.47 101.66 7.16 109.12
#5237 [0, 0, 0, -2172367197, 0] ≥ 7 ℤ/2ℤ 44.27 68.66 4.41 76.11
#5238 [0, 0, 0, 8689468788, 0] ≥ 7 ℤ/2ℤ 44.27 72.82 4.76 80.27
#5332 [0, 0, 0, -3984479037, 0] ≥ 7 ℤ/2ℤ 45.48 70.48 4.56 77.93
#5333 [0, 0, 0, 15937916148, 0] ≥ 7 ℤ/2ℤ 45.48 74.63 4.91 82.09
#5295 [0, 0, 0, 93833252100, 0] ≥ 7 ℤ/2ℤ 45.81 79.95 5.35 87.41
#5296 [0, 0, 0, -23458313025, 0] ≥ 7 ℤ/2ℤ 45.81 75.79 5.01 83.25
#5240 [0, 0, 0, -5198739777, 0] ≥ 7 ℤ/2ℤ 46.01 71.27 4.63 78.73
#5241 [0, 0, 0, 20794959108, 0] ≥ 7 ℤ/2ℤ 46.01 75.43 4.98 82.89
#4758 [0, 0, 0, -1577047042, 0] ≥ 7 ℤ/2ℤ 46.52 67.70 4.33 75.15
#4903 [0, 0, 0, 6308188168, 0] ≥ 7 ℤ/2ℤ 46.52 71.85 4.68 79.31
#5351 [0, 0, 0, -7236137601, 0] ≥ 7 ℤ/2ℤ 46.67 72.27 4.71 79.72
#5244 [0, 0, 0, -27843101517, 0] ≥ 7 ℤ/2ℤ 46.77 76.31 5.05 83.76
#5245 [0, 0, 0, 111372406068, 0] ≥ 7 ℤ/2ℤ 46.77 80.47 5.40 87.92
#5328 [0, 0, 0, 9140862843, 0] ≥ 7 ℤ/2ℤ 47.14 72.97 4.77 80.42
#5315 [0, 0, 0, 3211754495, 0] ≥ 7 ℤ/2ℤ 47.25 69.83 4.51 77.28
#5316 [0, 0, 0, -12847017980, 0] ≥ 7 ℤ/2ℤ 47.25 73.99 4.86 81.44
#5279 [0, 0, 0, 308655775428, 0] ≥ 7 ℤ/2ℤ 47.72 83.53 5.65 90.98
#5280 [0, 0, 0, -77163943857, 0] ≥ 7 ℤ/2ℤ 47.72 79.37 5.30 86.82
#5317 [0, 0, 0, -4304294841, 0] ≥ 7 ℤ/2ℤ 47.83 70.71 4.58 78.16
#5306 [0, 0, 0, -8816378537, 0] ≥ 7 ℤ/2ℤ 49.27 72.86 4.76 80.31
#5294 [0, 0, 0, 10617420723, 0] ≥ 7 ℤ/2ℤ 49.64 73.42 4.81 80.87
#5080 [0, 0, 0, 341120539683, 0] ≥ 7 ℤ/2ℤ 50.49 83.83 5.67 91.28
#5081 [0, 0, 0, -1364482158732, 0] ≥ 7 ℤ/2ℤ 50.49 87.98 6.02 95.44
#5246 [0, 0, 0, 39736873638, 0] ≥ 7 ℤ/2ℤ 50.77 77.38 5.14 84.83
#5278 [0, 0, 0, -21383686181, 0] ≥ 7 ℤ/2ℤ 51.04 75.52 4.98 82.97
#5276 [0, 0, 0, -15380890602, 0] ≥ 7 ℤ/2ℤ 51.07 74.53 4.90 81.98
#5277 [0, 0, 0, 61523562408, 0] ≥ 7 ℤ/2ℤ 51.07 78.69 5.25 86.14
#5082 [0, 0, 0, -345987474525, 0] ≥ 7 ℤ/2ℤ 51.19 83.87 5.68 91.32
#5083 [0, 0, 0, 1383949898100, 0] ≥ 7 ℤ/2ℤ 51.19 88.03 6.03 95.48
#5078 [0, 0, 0, 229187948913, 0] ≥ 7 ℤ/2ℤ 54.28 82.63 5.58 90.09
#5079 [0, 0, 0, -916751795652, 0] ≥ 7 ℤ/2ℤ 54.28 86.79 5.92 94.25
#2901 [0, 0, 0, -6360182823142…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 58.28 168.59 12.74 176.04
#4954 [0, 0, 0, 25440731292569…, 0] ≥ 7 ℤ/2ℤ 58.28 172.75 13.08 180.20
#5052 [0, 0, 0, -4887891348792…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 73.44 216.15 16.70 223.61
#5051 [0, 0, 0, -4272642074938…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 74.00 215.75 16.67 223.20
#5053 [0, 0, 0, -5801090061908…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 75.91 223.57 17.32 231.03
#5054 [0, 0, 0, -1393652428727…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 76.79 226.20 17.54 233.66
#5055 [0, 0, 0, -2909352827939…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 78.22 228.41 17.72 235.87
#5056 [0, 0, 0, -2979103222288…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 78.24 228.48 17.73 235.94
#5058 [0, 0, 0, -2164260278133…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 79.53 234.43 18.23 241.89
#5057 [0, 0, 0, -1216065811286…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 79.65 232.70 18.08 240.16
#5059 [0, 0, 0, -3071720608634…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 79.88 235.48 18.31 242.94
#5285 [0, 0, 0, 4097583, 0] ≥ 6 ℤ/2ℤ 31.72 49.84 2.84 57.29
#5286 [0, 0, 0, -16390332, 0] ≥ 6 ℤ/2ℤ 31.72 54.00 3.19 61.45
#5310 [0, 0, 0, 2020343, 0] ≥ 6 ℤ/2ℤ 32.50 47.72 2.67 55.17
#5311 [0, 0, 0, -8081372, 0] ≥ 6 ℤ/2ℤ 32.50 51.87 3.01 59.33
#5223 [0, 0, 0, -3129357, 0] ≥ 6 ℤ/2ℤ 33.38 49.03 2.78 56.48
#5224 [0, 0, 0, 12517428, 0] ≥ 6 ℤ/2ℤ 33.38 53.19 3.12 60.64
#5344 [0, 0, 0, 33024475, 0] ≥ 6 ℤ/2ℤ 34.87 56.10 3.36 63.55
#5345 [0, 0, 0, -132097900, 0] ≥ 6 ℤ/2ℤ 34.87 60.26 3.71 67.71
#5312 [0, 0, 0, 25254243, 0] ≥ 6 ℤ/2ℤ 35.36 55.29 3.30 62.75
#5314 [0, 0, 0, -101016972, 0] ≥ 6 ℤ/2ℤ 35.36 59.45 3.64 66.91
#5271 [0, 0, 0, -22008042, 0] ≥ 6 ℤ/2ℤ 35.78 54.88 3.26 62.33
#5272 [0, 0, 0, 88032168, 0] ≥ 6 ℤ/2ℤ 35.78 59.04 3.61 66.49
#5331 [0, 0, 0, 10220793, 0] ≥ 6 ℤ/2ℤ 36.44 52.58 3.07 60.03
#5302 [0, 0, 0, 101704948, 0] ≥ 6 ℤ/2ℤ 37.57 59.47 3.65 66.93
#5303 [0, 0, 0, -25426237, 0] ≥ 6 ℤ/2ℤ 37.57 55.31 3.30 62.77
#5304 [0, 0, 0, 157339828, 0] ≥ 6 ℤ/2ℤ 38.44 60.78 3.75 68.24
#5305 [0, 0, 0, -39334957, 0] ≥ 6 ℤ/2ℤ 38.44 56.62 3.41 64.08
#5288 [0, 0, 0, -4111371900, 0] ≥ 6 ℤ/2ℤ 39.55 70.57 4.57 78.02
#5293 [0, 0, 0, 1027842975, 0] ≥ 6 ℤ/2ℤ 39.55 66.41 4.22 73.87
#5071 [0, 0, 0, 1118207475, 0] ≥ 6 ℤ/2ℤ 39.72 66.66 4.24 74.12
#5072 [0, 0, 0, -4472829900, 0] ≥ 6 ℤ/2ℤ 39.72 70.82 4.59 78.28
#5274 [0, 0, 0, 1136987775, 0] ≥ 6 ℤ/2ℤ 39.75 66.71 4.25 74.17
#5275 [0, 0, 0, -4547951100, 0] ≥ 6 ℤ/2ℤ 39.75 70.87 4.60 78.33
#5231 [0, 0, 0, 55570438, 0] ≥ 6 ℤ/2ℤ 39.83 57.66 3.49 65.11
#5232 [0, 0, 0, -222281752, 0] ≥ 6 ℤ/2ℤ 39.83 61.82 3.84 69.27
#5287 [0, 0, 0, 181871613, 0] ≥ 6 ℤ/2ℤ 40.00 61.22 3.79 68.67
#5242 [0, 0, 0, -5591534025, 0] ≥ 6 ℤ/2ℤ 40.34 71.49 4.65 78.95
#5243 [0, 0, 0, 22366136100, 0] ≥ 6 ℤ/2ℤ 40.34 75.65 4.99 83.11
#5067 [0, 0, 0, 502545988, 0] ≥ 6 ℤ/2ℤ 40.76 64.26 4.04 71.72
#5070 [0, 0, 0, -125636497, 0] ≥ 6 ℤ/2ℤ 40.76 60.11 3.70 67.56
#5235 [0, 0, 0, -188116701, 0] ≥ 6 ℤ/2ℤ 41.57 61.32 3.80 68.77
#5236 [0, 0, 0, 752466804, 0] ≥ 6 ℤ/2ℤ 41.57 65.48 4.15 72.93
#5273 [0, 0, 0, -246030477, 0] ≥ 6 ℤ/2ℤ 42.11 62.12 3.87 69.58
#5233 [0, 0, 0, -398107437, 0] ≥ 6 ℤ/2ℤ 43.07 63.57 3.99 71.02
#5234 [0, 0, 0, 1592429748, 0] ≥ 6 ℤ/2ℤ 43.07 67.72 4.33 75.18
#5239 [0, 0, 0, -1035436017, 0] ≥ 6 ℤ/2ℤ 44.98 66.43 4.23 73.89
#4721 [0, 0, 0, -4371483958645…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 48.00 139.83 10.34 147.29
#4884 [0, 0, 0, 10928709896614…, 0] ≥ 6 ℤ/2ℤ 48.00 135.67 10.00 143.13
#5084 [0, 0, 0, 355832003268, 0] ≥ 6 ℤ/2ℤ 49.49 83.95 5.69 91.41
#5085 [0, 0, 0, -88958000817, 0] ≥ 6 ℤ/2ℤ 49.49 79.79 5.34 87.25
#5073 [0, 0, 0, -10741744797, 0] ≥ 6 ℤ/2ℤ 49.66 73.45 4.81 80.91
#5075 [0, 0, 0, 42966979188, 0] ≥ 6 ℤ/2ℤ 49.66 77.61 5.16 85.06
#5076 [0, 0, 0, -32502332577, 0] ≥ 6 ℤ/2ℤ 51.87 76.77 5.09 84.23
#5077 [0, 0, 0, 130009330308, 0] ≥ 6 ℤ/2ℤ 51.87 80.93 5.43 88.39
#4722 [0, 0, 0, -3778726822874…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 52.46 153.21 11.46 160.66
#4885 [0, 0, 0, 94468170571871…, 0] ≥ 6 ℤ/2ℤ 52.46 149.05 11.11 156.51
#4723 [0, 0, 0, -4440543488446…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 52.62 153.69 11.50 161.15
#4887 [0, 0, 0, 11101358721116…, 0] ≥ 6 ℤ/2ℤ 52.62 149.54 11.15 156.99
#4726 [0, 0, 0, -1541273056650…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 53.86 157.43 11.81 164.88
#4898 [0, 0, 0, 38531826416256…, 0] ≥ 6 ℤ/2ℤ 53.86 153.27 11.46 160.72
#4724 [0, 0, 0, -8991584786079…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.02 155.81 11.67 163.27
#4902 [0, 0, 0, 35966339144319…, 0] ≥ 6 ℤ/2ℤ 54.02 159.97 12.02 167.42
#4728 [0, 0, 0, -1836641446925…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.04 157.95 11.85 165.41
#4725 [0, 0, 0, -1421390128097…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.47 157.18 11.79 164.64
#4727 [0, 0, 0, -1675695255420…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.64 157.68 11.83 165.13
#4730 [0, 0, 0, -4353305005882…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.90 160.54 12.07 168.00
#4731 [0, 0, 0, -4566413080609…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.95 160.69 12.08 168.14
#4729 [0, 0, 0, -3221420605140…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 55.29 159.64 11.99 167.09
#4687 [0, 0, 0, -2826735674954…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 56.77 166.15 12.54 173.61
#4997 [0, 0, 0, -1438063816852…, 0] ≥ 6 ℤ/2ℤ 60.84 95.05 6.61 102.50