Elliptic Curve Rank Leaderboard

Congruent-number curves with rank lower bound ≥ 1

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showing 76 of 5563 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#2901 [0, 0, 0, -6360182823142…, 0] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 58.28 168.59 12.74 176.04
#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
#4721 [0, 0, 0, -4371483958645…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 48.00 139.83 10.34 147.29
#4722 [0, 0, 0, -3778726822874…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 52.46 153.21 11.46 160.66
#4723 [0, 0, 0, -4440543488446…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 52.62 153.69 11.50 161.15
#4726 [0, 0, 0, -1541273056650…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 53.86 157.43 11.81 164.88
#4724 [0, 0, 0, -8991584786079…, 0] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 54.02 155.81 11.67 163.27
#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
#5042 [0, 0, 0, -4323110629133…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 38.78 112.17 8.04 119.62
#4720 [0, 0, 0, -2330209058073…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 38.85 110.31 7.88 117.77
#5043 [0, 0, 0, -6226984745272…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 39.14 113.26 8.13 120.72
#5044 [0, 0, 0, -6472509822648…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 39.18 113.38 8.14 120.83
#5041 [0, 0, 0, -3448707957941…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 39.24 111.49 7.98 118.94
#5045 [0, 0, 0, -3529200367367…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 41.57 118.47 8.56 125.92
#5046 [0, 0, 0, -8569797165598…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 42.46 121.13 8.78 128.58
#5047 [0, 0, 0, -2296969090498…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 42.75 124.09 9.03 131.54
#5050 [0, 0, 0, -3192299787994…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 43.08 125.07 9.11 132.53
#5048 [0, 0, 0, -2587358715132…, 0] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 43.56 124.44 9.06 131.90
#15 [0, 0, 0, -856967076, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 23.34 65.87 4.18 73.32
#5033 [0, 0, 0, -2141283076, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 24.26 68.61 4.41 76.07
#5034 [0, 0, 0, -2185936516, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 24.28 68.67 4.41 76.13
#5035 [0, 0, 0, -3331021225, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 25.39 69.94 4.52 77.39
#5038 [0, 0, 0, -142221002884, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 28.45 81.20 5.46 88.66
#5036 [0, 0, 0, -107794679041, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 28.87 80.37 5.39 87.82
#5037 [0, 0, 0, -109482236161, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 28.88 80.42 5.39 87.87
#5040 [0, 0, 0, -292112144676, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 29.17 83.36 5.64 90.81
#5068 [0, 0, 0, -361386131716, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 29.39 84.00 5.69 91.45
#5069 [0, 0, 0, -371819452900, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 29.41 84.08 5.70 91.54
#5039 [0, 0, 0, -277645740241, 0] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 29.82 83.21 5.62 90.66
#4719 [0, 0, 0, -1572516, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 17.04 46.96 2.60 54.42
#5023 [0, 0, 0, -7695076, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 18.63 51.73 3.00 59.18
#5024 [0, 0, 0, -12264004, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 19.09 53.13 3.12 60.58
#5022 [0, 0, 0, -6786025, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 19.20 51.35 2.97 58.80
#5025 [0, 0, 0, -17631601, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.15 54.21 3.21 61.67
#5029 [0, 0, 0, -39513796, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.26 56.64 3.41 64.09
#5026 [0, 0, 0, -21799561, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.36 54.85 3.26 62.31
#5028 [0, 0, 0, -23961025, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.46 55.13 3.28 62.59
#5031 [0, 0, 0, -52272900, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.54 57.47 3.48 64.93
#5032 [0, 0, 0, -60310756, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 20.69 57.90 3.51 65.36
#5030 [0, 0, 0, -44502241, 0] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 21.08 56.99 3.44 64.45
#4718 [0, 0, 0, -1156, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 9.83 25.32 0.80 32.77
#5011 [0, 0, 0, -1681, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 10.89 26.44 0.89 33.90
#5012 [0, 0, 0, -4225, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 11.81 29.21 1.12 36.66
#5014 [0, 0, 0, -19044, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 12.63 33.72 1.50 41.18
#5017 [0, 0, 0, -23716, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 12.85 34.38 1.55 41.84
#5013 [0, 0, 0, -18769, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.31 33.68 1.50 41.13
#5019 [0, 0, 0, -37636, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.31 35.77 1.67 43.22
#5015 [0, 0, 0, -21025, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.42 34.02 1.52 41.47
#5020 [0, 0, 0, -44100, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.47 36.24 1.71 43.70
#5021 [0, 0, 0, -51076, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.61 36.68 1.75 44.14
#5018 [0, 0, 0, -25921, 0] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 13.63 34.65 1.58 42.10
#5000 [0, 0, 0, -36, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 6.36 14.91 -0.07 22.36
#4716 [0, 0, 0, -25, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 6.68 13.82 -0.16 21.27
#5002 [0, 0, 0, -49, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 7.36 15.83 0.01 23.29
#5004 [0, 0, 0, -196, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 8.05 19.99 0.36 27.45
#5003 [0, 0, 0, -169, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 8.60 19.55 0.32 27.00
#5005 [0, 0, 0, -225, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 8.88 20.41 0.39 27.86
#5007 [0, 0, 0, -484, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 8.95 22.71 0.58 30.16
#5006 [0, 0, 0, -441, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 9.55 22.43 0.56 29.88
#5010 [0, 0, 0, -900, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 9.57 24.57 0.74 32.02
#5008 [0, 0, 0, -529, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 9.74 22.97 0.60 30.43
#5009 [0, 0, 0, -841, 0] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 10.20 24.36 0.72 31.82