Elliptic Curve Rank Leaderboard

Curves with rank lower bound ≥ 3 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 143 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
#3437 [1, 0, 1, -1678579941468…, 26477982529328…] ≥ 8 ℤ/3ℤ 42.56 88.04 6.31 102.97
#1654 [1, 0, 1, -4714126488110…, 12457962738775…] ≥ 8 ℤ/3ℤ 43.54 87.39 6.46 106.07
#1099 [1, 0, 1, -4213613959455, 33284162329767…] ≥ 8 ℤ/3ℤ 43.61 83.61 5.96 98.82
#1356 [1, 0, 1, -2701783722667…, 17117286687159…] ≥ 8 ℤ/3ℤ 44.37 97.98 7.06 111.31
#1361 [1, 0, 1, -2840337686554…, 58189065087724…] ≥ 8 ℤ/3ℤ 45.43 91.13 6.50 104.55
#3454 [1, 0, 1, -2868867248090…, 59144422102587…] ≥ 8 ℤ/3ℤ 45.54 92.50 7.32 118.39
#3459 [1, 0, 1, -1369384199222…, 19491670055901…] ≥ 8 ℤ/3ℤ 45.74 88.27 6.29 102.36
#3462 [0, 1, 0, -9421065891357, 11092061421425…] ≥ 8 ℤ/3ℤ 46.37 88.79 6.26 101.24
#3846 [1, 0, 0, -3887029668612…, 30892653149264…] ≥ 8 ℤ/3ℤ 47.09 102.61 7.31 112.49
#3466 [1, 0, 1, -6295562671182…, 60808890567158…] ≥ 8 ℤ/3ℤ 47.19 98.31 7.20 113.84
#1357 [1, 0, 0, -6181201678011…, 59150317177246…] ≥ 8 ℤ/3ℤ 47.23 93.13 7.05 113.79
#1362 [1, 0, 1, -6188220593624…, 18744822957998…] ≥ 8 ℤ/3ℤ 47.95 92.36 6.65 106.88
#1355 [1, 0, 1, -8545991449498…, 96159706937086…] ≥ 8 ℤ/3ℤ 48.60 95.31 7.16 114.76
#1363 [0, 0, 0, -2145379042127…, 12099090944262…] ≥ 8 ℤ/3ℤ 50.44 95.87 6.95 110.61
#1358 [1, -1, 1, -5558495007053…, 15950871319686…] ≥ 8 ℤ/3ℤ 51.97 99.87 7.60 120.38
#1359 [1, -1, 1, -1844480924271…, 96418276905375…] ≥ 8 ℤ/3ℤ 52.19 100.82 8.76 137.79
#1360 [1, -1, 0, -1335312988286…, 18781146648346…] ≥ 8 ℤ/3ℤ 54.52 109.69 8.40 129.91
#3064 [0, 0, 0, 0, 70829139273819…] ≥ 8 ℤ/3ℤ 59.60 115.90 8.34 123.36
#1661 [1, 0, 1, -43204063985, 34565235981640…] ≥ 7 ℤ/3ℤ 35.81 66.94 4.72 85.08
#3440 [1, 0, 1, -955060908095, 35924746837868…] ≥ 7 ℤ/3ℤ 36.08 74.53 5.45 94.37
#3443 [1, 0, 1, -1644759495291…, 25674479247623…] ≥ 7 ℤ/3ℤ 36.43 80.17 6.09 102.91
#1335 [1, 0, 1, -810107314098, 27817151172835…] ≥ 7 ℤ/3ℤ 36.86 82.38 5.68 93.87
#3449 [0, 1, 1, -37352633327, 27778742222899…] ≥ 7 ℤ/3ℤ 37.28 69.65 4.78 84.64
#3453 [0, 0, 0, -97351728669, 32271012846809…] ≥ 7 ℤ/3ℤ 37.45 79.98 5.36 87.52
#3458 [1, 0, 1, -82065445090, 90186539123368…] ≥ 7 ℤ/3ℤ 37.46 74.54 5.07 87.01
#1336 [1, 0, 0, -2035462515005, 11177015596904…] ≥ 7 ℤ/3ℤ 37.47 79.72 5.72 96.64
#1337 [1, 0, 0, -1483566759815, 69627436452382…] ≥ 7 ℤ/3ℤ 37.75 82.10 5.75 95.69
#3469 [1, -1, 0, -1533725027976…, 23119028050726…] ≥ 7 ℤ/3ℤ 37.90 80.91 6.10 102.70
#3786 [1, -1, 0, -32988023466, 21769133846906…] ≥ 7 ℤ/3ℤ 37.95 74.60 4.97 84.27
#1338 [0, 1, 0, -180273846630, 29574795822924…] ≥ 7 ℤ/3ℤ 37.97 77.05 5.27 89.37
#1339 [1, -1, 0, -2346023850, 12480379081640…] ≥ 7 ℤ/3ℤ 38.06 80.19 5.36 87.65
#1340 [1, -1, 0, -3507651369384, 25281758312826…] ≥ 7 ℤ/3ℤ 38.06 82.71 5.90 98.27
#1341 [1, 0, 0, -4226087965313, 33363944130429…] ≥ 7 ℤ/3ℤ 38.38 85.97 6.04 98.83
#1342 [1, 0, 1, -4098927606262…, 10100739586409…] ≥ 7 ℤ/3ℤ 38.40 84.69 6.36 105.65
#1343 [1, 0, 0, -3710928957486, 27427679197387…] ≥ 7 ℤ/3ℤ 38.43 85.93 6.02 98.44
#1344 [1, -1, 0, -48749704665, 62871023029276…] ≥ 7 ℤ/3ℤ 38.51 78.25 5.22 86.28
#2923 [0, 0, 1, 0, 32742536500558…] ≥ 7 ℤ/3ℤ 45.01 86.73 5.91 94.18
#3435 [0, 1, 1, -9687757, 12256549127] ≥ 6 ℤ/3ℤ 26.97 50.26 2.94 59.98
#3439 [0, 1, 1, -925753397, 10841851921227] ≥ 6 ℤ/3ℤ 28.89 57.02 3.81 73.55
#1668 [1, -1, 0, -9026795691, 32997209797700…] ≥ 6 ℤ/3ℤ 29.10 65.80 4.44 80.38
#1320 [1, 0, 1, -6571364219, 20487437516462…] ≥ 6 ℤ/3ℤ 29.42 65.52 4.38 79.43
#1321 [1, 0, 1, -9641629029, 36439654520495…] ≥ 6 ℤ/3ℤ 29.60 61.22 4.31 80.58
#1322 [1, 0, 1, -5350645921, 15064423065516…] ≥ 6 ℤ/3ℤ 29.61 60.36 4.19 78.82
#3457 [1, 0, 0, -30023595887, 20022983602206…] ≥ 6 ℤ/3ℤ 29.62 66.80 4.66 83.99
#1323 [1, 0, 1, -1052379025, 13115318303120] ≥ 6 ℤ/3ℤ 29.65 60.91 3.96 73.94
#3464 [1, -1, 1, -374703419, 2783803557547] ≥ 6 ℤ/3ℤ 29.74 58.23 3.72 70.84
#3468 [1, 0, 0, -107483887227, 14193121444682…] ≥ 6 ℤ/3ℤ 29.91 78.01 5.26 87.91
#1314 [1, -1, 0, -663080916, 6572685336996] ≥ 6 ℤ/3ℤ 30.20 56.33 3.73 72.55
#1315 [1, -1, 0, -4058145576, 99508012617636] ≥ 6 ℤ/3ℤ 30.42 60.89 4.16 77.99
#1316 [1, 0, 1, -2525029950154, 15443648021985…] ≥ 6 ℤ/3ℤ 30.44 78.26 5.72 97.29
#1317 [1, 0, 0, -2970385626, 62367892354980] ≥ 6 ℤ/3ℤ 30.60 63.29 4.19 77.05
#1318 [1, 0, 1, -4587038098, 17350713393525…] ≥ 6 ℤ/3ℤ 30.68 71.00 4.62 79.10
#1319 [1, 0, 1, -170671598130, 24898868382347…] ≥ 6 ℤ/3ℤ 30.69 79.90 5.40 89.20
#2879 [0, 0, 1, 0, 15087003774597…] ≥ 6 ℤ/3ℤ 35.13 71.36 4.63 78.82
#2884 [0, 0, 1, 0, 24514990441382] ≥ 6 ℤ/3ℤ 35.51 67.73 4.32 75.18
#3434 [1, 0, 0, -22297742, 98226074116] ≥ 5 ℤ/3ℤ 21.63 56.50 3.40 64.14
#3438 [1, -1, 0, -324141, 89192321] ≥ 5 ℤ/3ℤ 21.86 41.67 2.18 50.13
#1295 [1, 0, 0, -83296293, 293440629889] ≥ 5 ℤ/3ℤ 22.84 53.71 3.34 66.33
#3445 [1, 0, 0, -127702, 333062436] ≥ 5 ℤ/3ℤ 22.92 45.31 2.46 52.77
#3448 [1, 0, 1, -40932715, 100783384482] ≥ 5 ℤ/3ℤ 23.53 48.37 3.05 64.20
#3451 [1, -1, 0, -16036386, 24883806968] ≥ 5 ℤ/3ℤ 23.62 49.60 2.96 61.40
#1291 [1, 0, 0, -24393911, 46686479785] ≥ 5 ℤ/3ℤ 23.83 50.89 3.07 62.66
#3461 [0, 1, 1, -30379967, 64440778455] ≥ 5 ℤ/3ℤ 24.05 40.49 2.79 63.30
#3463 [1, 0, 0, -199700187, 1086437663569] ≥ 5 ℤ/3ℤ 24.11 53.77 3.47 68.95
#1292 [1, 0, 0, -30606263, 79323080617] ≥ 5 ℤ/3ℤ 24.45 55.14 3.31 63.72
#1293 [1, 0, 0, -373911685, 2744591676225] ≥ 5 ℤ/3ℤ 24.55 59.78 3.78 70.83
#1294 [1, 0, 1, -947156853, 11219613159148] ≥ 5 ℤ/3ℤ 25.11 50.49 3.65 73.62
#1296 [1, 0, 1, -103938601, 377789890448] ≥ 5 ℤ/3ℤ 25.23 57.58 3.54 66.99
#1287 [1, 0, 0, -187559410, 3398634755972] ≥ 5 ℤ/3ℤ 25.41 63.69 3.99 71.23
#1288 [1, 0, 1, -1699035153, 16826142906256] ≥ 5 ℤ/3ℤ 25.62 67.43 4.32 75.37
#1289 [1, -1, 1, -196513427, 1051732985779] ≥ 5 ℤ/3ℤ 25.74 57.33 3.60 68.90
#1290 [1, 0, 0, -31400288, 238881825792] ≥ 5 ℤ/3ℤ 25.87 58.38 3.55 65.92
#1217 [1, 0, 1, -7652324, 346550615166] ≥ 5 ℤ/3ℤ 27.00 59.21 3.61 66.67
#1590 [1, 0, 1, -1402210, 638980920] ≥ 4 ℤ/3ℤ 16.24 32.61 2.05 54.07
#1591 [1, 0, 0, -59867, 10816849] ≥ 4 ℤ/3ℤ 16.58 38.15 1.87 45.92
#1592 [1, -1, 0, -29301, 1919681] ≥ 4 ℤ/3ℤ 16.59 31.04 1.40 42.47
#1593 [1, -1, 0, -52251, 2965013] ≥ 4 ℤ/3ℤ 16.78 36.22 1.72 44.21
#1594 [1, 0, 1, -2958745, 1969597352] ≥ 4 ℤ/3ℤ 17.28 44.37 2.53 56.33
#1595 [1, 0, 1, -121870, 17419212] ≥ 4 ℤ/3ℤ 17.37 37.27 1.85 46.87
#1596 [0, 1, 0, -283945, 57744600] ≥ 4 ℤ/3ℤ 17.38 37.53 1.96 49.28
#1597 [1, 0, 1, -28280, 2631530] ≥ 4 ℤ/3ℤ 17.39 34.98 1.62 43.09
#1598 [1, 0, 1, -100721, 12290520] ≥ 4 ℤ/3ℤ 17.46 31.50 1.59 46.17
#1599 [1, 0, 1, -325580, 71396382] ≥ 4 ℤ/3ℤ 17.63 36.15 1.92 49.69
#3785 [0, 0, 0, -22824, 1424529] ≥ 4 ℤ/3ℤ 18.00 32.38 1.44 41.86
#840 [1, 0, 1, -22988, 3286038] ≥ 4 ℤ/3ℤ 18.92 35.90 1.68 43.53
#841 [1, 0, 1, -24340, 3674062] ≥ 4 ℤ/3ℤ 19.03 36.13 1.70 43.76
#3410 [1, 0, 1, -139631351475, 20082708023947…] ≥ 4 ℤ/3ℤ 21.46 22.15 4.37 88.60
#842 [0, 1, 0, -103207958, 932064188713] ≥ 4 ℤ/3ℤ 24.14 60.98 3.77 68.64
#1505 [0, 0, 0, 174270951, 30369364569] ≥ 4 ℤ/3ℤ 27.52 61.09 3.78 68.54
#1154 [1, -1, 0, -3516, 81116] ≥ 3 ℤ/3ℤ 12.21 20.77 0.72 36.11
#1516 [1, 0, 0, -1282, 36036] ≥ 3 ℤ/3ℤ 12.29 26.79 0.92 34.51
#1517 [1, -1, 0, -199881, 34443873] ≥ 3 ℤ/3ℤ 12.39 31.69 1.70 48.23
#1518 [0, 1, 0, -76017, 8041744] ≥ 3 ℤ/3ℤ 12.43 24.95 1.35 45.33
#1519 [1, 0, 0, -107717, 14239681] ≥ 3 ℤ/3ℤ 12.55 36.58 1.81 46.47
#1520 [1, 0, 1, -37510, 2793012] ≥ 3 ℤ/3ℤ 12.57 24.04 1.21 43.21
#1521 [1, 0, 0, -145188, 21289744] ≥ 3 ℤ/3ℤ 12.58 32.68 1.68 47.27
#1522 [1, 0, 1, -7425, 1139492] ≥ 3 ℤ/3ℤ 12.64 33.91 1.51 41.42
#1152 [0, 0, 1, 306, 2135] ≥ 3 ℤ/3ℤ 12.64 22.06 0.52 28.86
#1153 [0, 1, 0, -2873, 58312] ≥ 3 ℤ/3ℤ 12.65 20.30 0.68 35.50
#2813 [1, 0, 1, -2708, 61518] ≥ 3 ℤ/3ℤ 12.78 26.65 0.95 35.58
#2824 [0, 1, 1, -23777, 1402920] ≥ 3 ℤ/3ℤ 12.93 26.83 1.21 41.84
#2817 [0, 1, 0, -11517, 471871] ≥ 3 ℤ/3ℤ 13.01 23.44 0.99 39.67
#2820 [1, 0, 1, -19721, 1064280] ≥ 3 ℤ/3ℤ 13.07 20.63 1.01 41.28
#3759 [0, 1, 1, -73844607, 244220728125] ≥ 3 ℤ/3ℤ 16.49 16.49 2.63 65.97