Elliptic Curve Rank Leaderboard

Quartic twists with rank lower bound ≥ 8

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showing 68 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