Elliptic Curve Rank Leaderboard

Curves with torsion ℤ/12ℤ

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showing 53 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1105 [1, 0, 0, -4422329901784…, 98943710602886…] ≥ 4 ℤ/12ℤ 61.14 318.02 25.23 326.92
#1102 [1, -1, 1, -4240375358253…, 10627414422800…] ≥ 3 ℤ/12ℤ 36.39 172.19 13.40 188.64
#1104 [1, 0, 0, -2015047724010…, 34815737557101…] ≥ 3 ℤ/12ℤ 36.80 207.46 16.56 227.86
#1103 [1, 0, 0, 22560435880391…, 54047983322613…] ≥ 3 ℤ/12ℤ 36.87 184.45 14.05 191.89
#2139 [1, 0, 0, -1586501772830…, 29755509382256…] ≥ 3 ℤ/12ℤ 37.60 187.78 14.33 195.31
#2143 [1, -1, 1, -3014826139222…, 20148444419078…] ≥ 3 ℤ/12ℤ 37.95 178.05 14.74 208.34
#2137 [1, 0, 0, -2193596698337…, 12865671330093…] ≥ 3 ℤ/12ℤ 38.26 183.28 14.05 193.63
#2140 [1, 0, 0, -1819834111904…, 36464739063950…] ≥ 3 ℤ/12ℤ 38.43 191.75 14.69 200.32
#1493 [1, 0, 0, -1058306588646…, -1317017242620…] ≥ 3 ℤ/12ℤ 38.71 227.88 17.82 239.74
#1494 [1, 0, 0, -1210057483793…, 12237572864806…] ≥ 3 ℤ/12ℤ 39.07 218.03 16.88 226.33
#1490 [1, -1, 1, -9215871878203…, 31327842129454…] ≥ 3 ℤ/12ℤ 39.14 201.76 15.49 209.22
#2141 [1, 0, 0, -2744874623003…, 80881651709627…] ≥ 3 ℤ/12ℤ 40.09 189.80 14.50 197.31
#1492 [1, 0, 0, -9133867357763…, 58989289700011…] ≥ 3 ℤ/12ℤ 41.94 217.66 16.84 225.48
#2142 [1, 0, 0, -5447532560530…, 15475612753269…] ≥ 3 ℤ/12ℤ 42.20 192.85 15.57 217.02
#2145 [1, 0, 0, -1501450481401…, 70813267432828…] ≥ 3 ℤ/12ℤ 43.87 196.97 16.77 233.88
#1491 [1, 0, 0, -3531474678706…, 25483174836382…] ≥ 3 ℤ/12ℤ 44.08 209.82 16.36 222.63
#1118 [1, 0, 0, -233489241305, 43447031653412…] ≥ 2 ℤ/12ℤ 17.42 75.76 5.26 90.14
#1403 [1, 0, 1, -2403398329689…, 45350987272091…] ≥ 2 ℤ/12ℤ 18.45 97.03 8.28 131.68
#1404 [1, 0, 0, -4090073014536…, -4342979566325…] ≥ 2 ℤ/12ℤ 18.46 105.07 7.45 112.55
#1406 [1, -1, 0, -1539820774172…, 23256983382057…] ≥ 2 ℤ/12ℤ 19.57 84.91 7.06 116.52
#1408 [1, -1, 1, -4057036973897…, 99463223712366…] ≥ 2 ℤ/12ℤ 19.81 113.47 8.69 133.25
#1410 [1, 0, 0, 21751791658340…, 11120816542361…] ≥ 2 ℤ/12ℤ 20.46 135.24 9.95 142.68
#2150 [1, 0, 1, -9898992704351…, 11987665597097…] ≥ 2 ℤ/12ℤ 20.52 94.37 8.06 129.01
#1405 [1, 0, 0, 11026817040553…, -7651093618760…] ≥ 2 ℤ/12ℤ 21.69 108.33 7.72 115.52
#1407 [1, 0, 0, -7159242129940…, 23315712344538…] ≥ 2 ℤ/12ℤ 22.05 90.42 7.46 121.14
#1409 [1, 0, 0, -1184200349242…, 15685104898890…] ≥ 2 ℤ/12ℤ 22.51 110.24 8.40 129.55
#2151 [1, -1, 1, -1017251341732…, 12487375828482…] ≥ 2 ℤ/12ℤ 22.75 112.32 8.43 129.10
#2149 [1, 0, 0, -1891977980095…, 17409937568236…] ≥ 2 ℤ/12ℤ 22.87 103.48 7.32 111.34
#2148 [1, 0, 0, -1615407595597…, -3038669284740…] ≥ 2 ℤ/12ℤ 23.44 115.96 8.36 123.58
#2153 [1, 0, 0, 13251942619071…, 11769468889121…] ≥ 2 ℤ/12ℤ 24.30 117.14 8.45 124.37
#2154 [1, 0, 0, -1246849572154…, 53588204298205…] ≥ 2 ℤ/12ℤ 24.37 100.70 8.68 136.62
#2155 [1, 0, 0, -1115243298136…, 14335160068685…] ≥ 2 ℤ/12ℤ 24.96 105.07 9.19 143.19
#1055 [1, 0, 0, -471900, 124722000] ≥ 1 ℤ/12ℤ 8.36 34.83 1.93 50.81
#1060 [1, 0, 0, -2096146, 1124611076] ≥ 1 ℤ/12ℤ 8.80 45.21 2.53 55.28
#1068 [1, 0, 0, -749461, 263897441] ≥ 1 ℤ/12ℤ 10.31 42.60 2.30 52.31
#1075 [1, 0, 1, -10696531938, 42580565978515…] ≥ 1 ℤ/12ℤ 11.51 59.81 4.30 80.89
#1809 [1, -1, 1, -119815963367, 15963236505248…] ≥ 1 ℤ/12ℤ 11.96 63.36 4.82 88.14
#1081 [1, 0, 0, -32075535, 63675551097] ≥ 1 ℤ/12ℤ 12.52 54.24 3.26 63.46
#1082 [1, 0, 1, -786170938, 8484377935088] ≥ 1 ℤ/12ℤ 12.54 51.86 3.64 73.06
#2156 [1, -1, 1, -9403464137, 35155184024864…] ≥ 1 ℤ/12ℤ 12.72 67.33 4.50 80.51
#1814 [1, -1, 1, 7958928568, -3113366597164…] ≥ 1 ℤ/12ℤ 12.98 73.38 4.80 80.27
#1812 [1, 0, 0, -4158299670, 73902056818212] ≥ 1 ℤ/12ℤ 13.25 69.89 4.53 78.06
#1811 [1, 0, 0, 79316545, 1678407056025] ≥ 1 ℤ/12ℤ 14.06 62.39 3.88 69.82
#1813 [1, 0, 0, 259431824, 12722468380448…] ≥ 1 ℤ/12ℤ 14.89 71.02 4.60 78.48
#2157 [1, 0, 0, -189359882011, 31716103409183…] ≥ 1 ℤ/12ℤ 16.83 66.38 4.97 89.51
#1810 [1, 0, 0, -6126044669401…, 18449277465063…] ≥ 1 ℤ/12ℤ 17.23 92.04 6.64 106.85
#879 [1, -1, 1, -122, 1721] ≥ 0 ℤ/12ℤ 4.50 20.84 0.42 28.39
#1008 [1, 0, 1, 1922, 20756] ≥ 0 ℤ/12ℤ 5.35 27.18 0.95 34.30
#1050 [1, 0, 0, -25725, 1577457] ≥ 0 ℤ/12ℤ 7.91 30.09 1.35 42.08
#1063 [1, -1, 1, -20391107, 35440483331] ≥ 0 ℤ/12ℤ 9.01 46.64 2.89 62.11
#1072 [1, 0, 0, -167843570, 843125287812] ≥ 0 ℤ/12ℤ 11.05 56.76 3.56 68.44
#1077 [1, -1, 1, -475589417, 3992151134441] ≥ 0 ℤ/12ℤ 11.68 52.66 3.57 71.55
#1078 [1, 0, 1, -80216838, 341267523688] ≥ 0 ℤ/12ℤ 11.74 58.11 3.56 66.64