Elliptic Curve Rank Leaderboard

Curves with rank lower bound ≥ 9 and torsion ℤ/4ℤ

Click a column header to sort; click again to reverse. Curves missing a value (no primes of bad reduction supplied yet) sort last.

Download the database (JSON) ↓

showing 81 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1919 [1, 1, 1, -6256786656374…, 19049126547136…] ≥ 13 ℤ/4ℤ 145.51 374.59 30.61 397.04
#1918 [1, -1, 1, -1844990787237…, 96445313848956…] ≥ 13 ℤ/4ℤ 145.94 384.61 31.06 400.29
#803 [0, -1, 0, -8932110013773…, 32231848935325…] ≥ 13 ℤ/4ℤ 154.65 372.70 29.88 384.29
#3179 [1, 1, 1, -2842233550864…, 17952730709933…] ≥ 13 ℤ/4ℤ 154.68 391.18 31.37 401.58
#325 [0, 1, 0, -1014448194215…, 38021628663351…] ≥ 13 ℤ/4ℤ 157.83 402.12 32.28 412.31
#3704 [0, 1, 0, -1017623839762…, 39275012198212…] ≥ 12 ℤ/4ℤ 106.49 276.10 21.84 287.98
#1921 [1, 0, 0, -1086750289534…, 43597316571532…] ≥ 12 ℤ/4ℤ 107.05 286.66 22.88 301.99
#3562 [1, -1, 1, -2037619837783…, 34753468662079…] ≥ 12 ℤ/4ℤ 109.87 272.38 21.49 283.15
#3705 [1, 0, 0, -7447528317264…, 24734767791049…] ≥ 12 ℤ/4ℤ 113.28 299.00 23.93 314.67
#1125 [1, 1, 1, -2044361857832…, 11659777722440…] ≥ 12 ℤ/4ℤ 115.96 307.64 24.40 317.77
#3706 [1, -1, 1, -1743521616453…, 88610196487924…] ≥ 12 ℤ/4ℤ 131.34 326.80 26.37 344.85
#3598 [1, -1, 0, -1016169161922…, 12464279528163…] ≥ 11 ℤ/4ℤ 84.14 210.93 16.55 225.80
#3518 [1, 1, 1, -7671715934167…, 81782853545083…] ≥ 11 ℤ/4ℤ 86.19 208.42 16.42 224.96
#3702 [1, 0, 0, -3809385349733…, 88199784154175…] ≥ 11 ℤ/4ℤ 90.08 219.32 17.05 229.77
#1098 [0, -1, 0, -2898873654461…, 20921846641378…] ≥ 11 ℤ/4ℤ 91.34 240.67 18.79 249.86
#3703 [1, -1, 0, -7611294031803…, 25157222715082…] ≥ 11 ℤ/4ℤ 93.46 234.73 18.36 245.66
#1922 [1, 1, 1, -1092009163246…, 43765149405799…] ≥ 11 ℤ/4ℤ 96.05 234.35 18.38 246.74
#3156 [0, 1, 0, -9815797255264…, 17173523831080…] ≥ 11 ℤ/4ℤ 96.39 245.97 19.20 254.07
#3162 [0, 0, 0, -7101645059837…, 72620199964540…] ≥ 11 ℤ/4ℤ 97.38 239.80 18.85 252.36
#3151 [0, 0, 0, -9443503407019…, 35198221052740…] ≥ 11 ℤ/4ℤ 97.82 247.71 19.50 260.12
#3159 [1, 0, 0, -2046128832176…, 11264588019995…] ≥ 11 ℤ/4ℤ 98.25 259.99 20.71 276.26
#3158 [1, 1, 1, -9616802040765…, 11458141648950…] ≥ 11 ℤ/4ℤ 99.29 254.00 20.05 267.08
#3153 [1, 0, 0, -8359895892458…, 29455847563502…] ≥ 11 ℤ/4ℤ 99.41 260.09 20.58 273.57
#3149 [1, 0, 1, -2560843813858…, 48850271826555…] ≥ 11 ℤ/4ℤ 102.16 259.37 20.40 270.02
#3148 [1, 1, 1, -2186722332011…, 39354506601874…] ≥ 11 ℤ/4ℤ 105.35 253.59 20.16 269.55
#3142 [1, 0, 0, -6154113222947…, 55387192211873…] ≥ 11 ℤ/4ℤ 107.05 269.91 21.24 279.56
#3133 [1, -1, 1, -6733405851080…, 48003254557985…] ≥ 11 ℤ/4ℤ 111.37 299.29 23.65 307.46
#3139 [1, 0, 0, -1234140270416…, 52744760628030…] ≥ 11 ℤ/4ℤ 112.19 288.00 22.95 302.37
#3136 [1, 0, 0, -1680730071967…, 26485415853243…] ≥ 11 ℤ/4ℤ 113.33 296.84 23.64 310.20
#3128 [1, 1, 1, -2435109968648…, 46251325990521…] ≥ 11 ℤ/4ℤ 116.31 305.97 24.70 325.13
#3124 [1, -1, 1, -5955267645195…, 20740471281776…] ≥ 11 ℤ/4ℤ 126.40 333.19 26.49 341.95
#3126 [1, 0, 0, -1016348547453…, 12471286206505…] ≥ 11 ℤ/4ℤ 126.99 316.45 25.61 336.33
#3122 [1, -1, 1, -2531176936083…, 48928612825281…] ≥ 11 ℤ/4ℤ 128.54 325.96 26.05 339.06
#3120 [1, -1, 1, -6530796764529…, 67765566660616…] ≥ 11 ℤ/4ℤ 139.11 366.81 29.32 376.55
#632 [0, 1, 0, 53659646002842…, 14610806763317…] ≥ 10 ℤ/4ℤ 69.33 177.32 13.46 184.67
#1933 [1, 1, 1, -1787947782144…, 91941993506861…] ≥ 10 ℤ/4ℤ 70.63 179.12 13.85 192.96
#3695 [0, 0, 0, -1018772800122…, 38923083106512…] ≥ 10 ℤ/4ℤ 74.72 180.40 13.83 191.27
#3696 [1, 0, 0, -1018145777293…, 39205652896580…] ≥ 10 ℤ/4ℤ 75.70 207.37 16.10 218.90
#3697 [0, 0, 0, -2930883034151…, 19310407237232…] ≥ 10 ℤ/4ℤ 76.18 192.51 15.06 208.26
#3698 [1, 1, 0, -9707860480137…, 36511148543945…] ≥ 10 ℤ/4ℤ 76.26 193.38 14.94 204.94
#3699 [1, -1, 1, -2383088857743…, 13656594080685…] ≥ 10 ℤ/4ℤ 77.05 197.52 15.23 207.64
#3700 [1, 1, 1, -4959610099322…, 13440049851581…] ≥ 10 ℤ/4ℤ 77.61 201.77 15.79 216.74
#3701 [0, 1, 0, -1636853509520…, 85417472014584…] ≥ 10 ℤ/4ℤ 78.06 210.77 16.31 220.44
#3681 [1, -1, 1, -3266529867562…, 71297354488784…] ≥ 10 ℤ/4ℤ 78.51 203.87 15.81 215.49
#3682 [1, -1, 1, -1186276992820…, 15312238856253…] ≥ 10 ℤ/4ℤ 79.04 202.04 15.61 212.45
#3683 [0, 0, 0, -1219617061196…, 51842148918110…] ≥ 10 ℤ/4ℤ 79.29 198.66 15.85 219.44
#3684 [1, 0, 0, -2722795982203…, 54676988991001…] ≥ 10 ℤ/4ℤ 79.91 213.21 16.77 228.76
#3685 [1, -1, 1, -1243763883354…, 53268817207731…] ≥ 10 ℤ/4ℤ 80.55 206.64 16.10 219.50
#3103 [0, 1, 0, -1109077055513…, 14209200477703…] ≥ 10 ℤ/4ℤ 80.97 197.90 15.44 212.25
#3686 [0, 0, 0, -1518426308912…, 72017587023559…] ≥ 10 ℤ/4ℤ 81.13 198.30 15.88 220.10
#3687 [0, 0, 0, -3123539885838…, 21246218309025…] ≥ 10 ℤ/4ℤ 81.22 206.13 16.21 222.26
#3101 [1, 0, 0, -8736253981243…, 12416084781715…] ≥ 10 ℤ/4ℤ 87.35 227.48 17.64 235.00
#3100 [0, 1, 0, -5049106139198…, 13566369958791…] ≥ 10 ℤ/4ℤ 89.49 219.80 17.11 230.61
#3098 [0, 0, 0, -2901413377029…, 60112620677766…] ≥ 10 ℤ/4ℤ 92.17 228.71 17.99 242.77
#3097 [1, 0, 0, -1281493142199…, 20908478821228…] ≥ 10 ℤ/4ℤ 92.82 231.95 18.05 240.65
#3088 [0, 1, 0, -1893054759558…, 74333357526273…] ≥ 10 ℤ/4ℤ 93.56 240.14 18.72 248.39
#3094 [1, 0, 0, -1034642810304…, 27194354320720…] ≥ 10 ℤ/4ℤ 93.58 233.47 18.15 241.18
#3090 [1, -1, 1, -2856201689245…, 18556040321240…] ≥ 10 ℤ/4ℤ 96.41 236.18 18.58 249.63
#3694 [1, -1, 1, -3133455566469…, 65603644346627…] ≥ 9 ℤ/4ℤ 60.75 177.39 13.56 187.73
#1934 [1, -1, 1, -1259556984679…, 17205797813043…] ≥ 9 ℤ/4ℤ 60.86 161.73 12.92 185.00
#3673 [0, 1, 0, 24931835892509…, 43709472859500…] ≥ 9 ℤ/4ℤ 61.55 170.21 12.86 177.65
#3674 [1, -1, 1, -7361864201747…, 24312510518475…] ≥ 9 ℤ/4ℤ 62.92 165.97 13.34 190.30
#3675 [1, -1, 1, -1272436048402…, 54847418658071…] ≥ 9 ℤ/4ℤ 63.05 166.43 12.69 178.12
#3676 [0, 0, 0, -5370287529643…, 15105507386846…] ≥ 9 ℤ/4ℤ 63.40 162.89 12.44 175.53
#3677 [1, 1, 0, -2865810038344…, 19644296442869…] ≥ 9 ℤ/4ℤ 63.47 170.87 12.99 180.66
#3678 [0, 0, 0, -1154028987379…, 47687482275649…] ≥ 9 ℤ/4ℤ 63.48 163.68 12.58 177.83
#3679 [1, -1, 1, 21979255745287…, -2076828894260…] ≥ 9 ℤ/4ℤ 63.59 165.64 12.49 172.85
#3680 [1, 1, 1, -1841939043304…, 96219033267427…] ≥ 9 ℤ/4ℤ 64.09 154.18 12.41 179.23
#2084 [1, 1, 1, 53966300098701…, 71923413689649…] ≥ 9 ℤ/4ℤ 64.12 157.38 11.79 164.83
#2093 [0, 0, 0, -1259741485178…, 54421468413519…] ≥ 9 ℤ/4ℤ 64.96 153.07 12.31 178.09
#1173 [1, 0, 1, -1742907593966…, 88443868698507…] ≥ 9 ℤ/4ℤ 66.84 165.71 12.71 179.07
#3074 [1, -1, 1, -1766206539740…, 90341467476381…] ≥ 9 ℤ/4ℤ 66.87 176.32 13.75 192.92
#3073 [0, -1, 0, -6310113763199…, 19134146811238…] ≥ 9 ℤ/4ℤ 72.31 178.27 13.68 189.83
#2098 [1, 0, 0, -7967320834038…, 26976176262494…] ≥ 9 ℤ/4ℤ 73.16 220.98 17.21 231.98
#2099 [1, 0, 0, 55634371339019…, -2765121350121…] ≥ 9 ℤ/4ℤ 73.16 230.62 17.91 237.81
#2096 [0, 1, 0, -9825609019887…, 37487573620515…] ≥ 9 ℤ/4ℤ 79.14 227.23 20.00 274.06
#2103 [0, 1, 0, -6128849579934…, 58817774891634…] ≥ 9 ℤ/4ℤ 79.14 254.03 20.00 265.75
#3067 [0, -1, 0, -1627567332692…, 22374180470634…] ≥ 9 ℤ/4ℤ 81.55 205.70 15.82 213.16
#3069 [1, 0, 0, -7914107241966…, 27098533249188…] ≥ 9 ℤ/4ℤ 83.24 200.05 15.81 218.14
#2097 [1, 0, 0, -1352161593194…, 60514755240142…] ≥ 9 ℤ/4ℤ 87.09 286.29 22.90 302.64
#2102 [1, 0, 0, 33112058816367…, 32163354268157…] ≥ 9 ℤ/4ℤ 87.09 298.95 23.60 305.99