Elliptic Curve Rank Leaderboard

Curves with rank lower bound ≥ 9 and torsion ℤ/3ℤ

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 39 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#318 [1, 0, 1, -1074047301641…, 48976939778870…] ≥ 15 ℤ/3ℤ 145.16 331.53 26.31 339.06
#1936 [0, 1, 1, -2479143454512…, 47463673909255…] ≥ 14 ℤ/3ℤ 112.22 256.27 20.27 269.92
#1935 [1, 0, 1, -1886778476063…, 99753805569209…] ≥ 14 ℤ/3ℤ 132.31 306.99 25.09 331.27
#1937 [1, 0, 1, -3142617982476…, 67755045622702…] ≥ 13 ℤ/3ℤ 101.42 242.92 19.17 256.82
#1938 [1, 0, 1, -2557499874808…, 49997987268990…] ≥ 13 ℤ/3ℤ 103.14 230.19 18.03 242.40
#3181 [1, 0, 0, -7326277178801…, 24059879080163…] ≥ 13 ℤ/3ℤ 121.40 260.66 20.58 273.17
#3177 [1, 0, 0, -3582219213057…, 26097195687506…] ≥ 13 ℤ/3ℤ 126.09 274.87 21.98 291.75
#3175 [1, 0, 0, -2451596981881…, 15101910099026…] ≥ 13 ℤ/3ℤ 127.37 266.24 20.97 276.84
#45 [1, 0, 0, -5607159337021…, 52994280301716…] ≥ 13 ℤ/3ℤ 127.97 269.24 21.20 279.35
#3174 [1, 0, 0, -7032750154590…, 23482511052116…] ≥ 13 ℤ/3ℤ 129.34 276.75 21.83 286.94
#1939 [1, 0, 0, -1757435272012…, 20803849458555…] ≥ 12 ℤ/3ℤ 108.24 246.85 19.28 255.08
#1194 [1, 0, 0, -1507573912593…, 71948127291473…] ≥ 12 ℤ/3ℤ 111.82 236.33 18.51 247.73
#3171 [1, 0, 1, -6999312010100…, 76392581201931…] ≥ 12 ℤ/3ℤ 115.55 242.95 18.99 252.45
#3168 [1, 0, 1, -8108955275569…, 28126393626819…] ≥ 12 ℤ/3ℤ 119.90 259.50 20.55 273.48
#3167 [1, 0, 0, -2886947269588…, 64622389720504…] ≥ 12 ℤ/3ℤ 120.33 261.16 20.50 270.54
#3169 [1, 0, 1, -5101239509115…, 76434974688414…] ≥ 12 ℤ/3ℤ 121.10 249.60 19.48 257.06
#3166 [1, 0, 1, -2272042537611…, 13180898673869…] ≥ 12 ℤ/3ℤ 125.04 260.15 20.73 276.57
#1195 [1, 0, 0, -1938140500023…, 32840137866325…] ≥ 11 ℤ/3ℤ 77.19 169.60 13.20 186.29
#3163 [1, -1, 0, -4536184139377…, 11775693851525…] ≥ 11 ℤ/3ℤ 94.31 189.32 14.67 202.66
#3161 [0, 0, 0, -2902707625457…, 19045970977668…] ≥ 11 ℤ/3ℤ 104.72 207.82 16.26 222.04
#3165 [0, 0, 1, 0, 44182596082121…] ≥ 11 ℤ/3ℤ 118.99 234.69 18.24 242.15
#1395 [1, 0, 0, -2128393013738…, 11958849002784…] ≥ 10 ℤ/3ℤ 61.77 137.87 10.43 152.04
#1196 [1, 0, 1, -1283794281755…, 55987935129057…] ≥ 10 ℤ/3ℤ 67.39 145.75 11.31 164.33
#3104 [1, 0, 0, -3869089858037…, 71645473412331…] ≥ 10 ℤ/3ℤ 76.94 180.00 13.71 188.37
#3107 [0, 0, 0, 0, 46927269375243…] ≥ 10 ℤ/3ℤ 82.21 161.13 12.11 168.59
#3859 [1, 0, 0, -7114057665400…, 76205206958176…] ≥ 10 ℤ/3ℤ 83.53 201.04 15.51 211.00
#3865 [1, 0, 0, -1515093861677…, 66596247814828…] ≥ 10 ℤ/3ℤ 91.75 210.67 16.30 220.09
#3788 [1, 0, 1, -1461285343169…, 21489517033413…] ≥ 9 ℤ/3ℤ 52.23 115.85 8.60 130.18
#3787 [0, 1, 0, 35111895184806…, 17059676504171…] ≥ 9 ℤ/3ℤ 55.88 108.47 7.72 115.91
#1647 [1, -1, 1, -1371407722296…, 71308803097251…] ≥ 9 ℤ/3ℤ 56.24 114.52 8.27 123.37
#1197 [1, 0, 1, -1892251104922…, 31686836332788…] ≥ 9 ℤ/3ℤ 58.06 129.17 9.77 144.77
#3077 [1, 0, 0, -6811796873298…, 68773456615953…] ≥ 9 ℤ/3ℤ 61.62 143.47 10.80 155.53
#3447 [1, 0, 0, -8292485875462…, 34176182904426…] ≥ 9 ℤ/3ℤ 61.90 126.98 9.30 135.72
#3847 [1, 0, 0, -1680783198275…, 26824639618179…] ≥ 9 ℤ/3ℤ 62.02 133.19 9.91 144.44
#3848 [1, 0, 1, -6029378056131…, 18052229057559…] ≥ 9 ℤ/3ℤ 63.95 135.16 10.15 148.25
#3858 [1, 0, 0, -4996847017008…, 14298452464795…] ≥ 9 ℤ/3ℤ 64.26 137.99 10.25 147.79
#1643 [0, 0, 0, 0, 30457819633596…] ≥ 9 ℤ/3ℤ 69.17 137.24 10.12 144.70
#3080 [0, 0, 1, 0, 87299817093221…] ≥ 9 ℤ/3ℤ 78.23 153.16 11.44 160.62
#3081 [0, 0, 0, 0, 19988905798337…] ≥ 9 ℤ/3ℤ 88.37 177.84 13.50 185.30