Elliptic Curve Rank Leaderboard

Curves with rank lower bound ≥ 3 and torsion ℤ/2ℤ × ℤ/4ℤ

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showing 135 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1827 [1, 0, 0, -1604573174364…, -3694491204583…] ≥ 9 ℤ/2ℤ × ℤ/4ℤ 73.16 226.37 17.56 234.08
#1107 [0, 1, 0, -6141005737705…, 58574331773488…] ≥ 9 ℤ/2ℤ × ℤ/4ℤ 79.14 242.33 19.65 265.74
#1828 [1, 0, 0, -1443705842368…, 51852453412695…] ≥ 9 ℤ/2ℤ × ℤ/4ℤ 87.09 294.46 23.25 302.84
#3063 [0, 1, 0, -8665851076482…, 93941596539042…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 55.74 173.95 13.26 183.88
#1108 [0, 1, 0, -2368606183248…, 14012948260726…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 62.29 194.20 15.08 207.62
#1109 [1, 0, 0, -6565665805280…, 20476368651145…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 62.42 200.43 15.79 217.58
#3057 [1, 0, 0, -2324040155254…, 39035737383640…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 65.50 219.12 16.99 228.28
#3051 [1, 1, 1, -1839926530538…, 29873101006545…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 66.36 230.53 18.00 241.40
#3062 [0, -1, 0, -1556209069050…, 23529944481555…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 66.92 201.03 15.60 213.27
#3041 [1, 0, 0, -7408020279205…, 24516259632532…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 68.87 218.12 17.09 231.76
#3048 [0, -1, 0, -8668931524503…, 61220734062068…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 69.61 210.92 16.27 218.42
#3039 [1, 0, 0, -2606368822937…, 50137806027135…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 69.66 217.99 16.95 228.63
#3027 [1, 0, 0, -9301637973794…, 24817682032962…] ≥ 8 ℤ/2ℤ × ℤ/4ℤ 70.77 224.26 17.40 232.44
#1089 [0, 1, 0, -5334348061487…, 14972113589959…] ≥ 7 ℤ/2ℤ × ℤ/4ℤ 46.09 148.49 11.27 161.70
#1830 [0, 1, 0, -2386801266816…, 44845424005663…] ≥ 7 ℤ/2ℤ × ℤ/4ℤ 48.52 145.41 11.04 159.29
#2934 [1, 1, 1, -8007418165950…, -8707164374817…] ≥ 7 ℤ/2ℤ × ℤ/4ℤ 54.66 176.18 13.37 183.64
#2930 [1, 1, 1, -9969335425497…, 36738166741349…] ≥ 7 ℤ/2ℤ × ℤ/4ℤ 58.44 181.23 13.86 191.21
#2926 [0, 1, 0, -4123297792196…, 83669201239698…] ≥ 7 ℤ/2ℤ × ℤ/4ℤ 61.15 193.80 14.87 202.37
#3484 [0, -1, 0, -9543695128779…, 11343572956219…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 38.14 128.13 9.63 142.72
#3483 [0, 1, 0, -2474617489821…, 14983292255697…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 38.67 120.02 9.17 138.67
#3801 [0, 1, 0, -7460731221246…, 88653323868322…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 38.85 127.48 9.32 135.07
#2152 [0, -1, 0, -7602351178123…, 80680442961959…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 39.33 122.84 9.44 142.04
#3805 [0, 1, 0, -2701980700587…, 14820640627240…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 40.64 130.09 9.57 138.94
#3806 [0, 1, 0, -2013725795072…, 64729589895519…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 40.74 130.17 9.55 138.05
#1826 [0, -1, 0, -3436336410579…, 36692720733182…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 40.78 125.04 9.12 132.75
#3798 [1, 0, 0, -2213303074744…, 17321055963451…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 41.04 123.77 9.01 131.43
#1111 [0, 1, 0, -2013664127615…, -6494465861707…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 41.33 130.17 9.55 138.05
#1112 [1, 0, 0, -6450655325320…, 18285491619516…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 41.41 125.35 9.18 134.64
#3808 [1, 1, 1, -1590515024185…, 76561522426333…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 41.78 125.79 9.30 137.35
#3807 [0, -1, 0, -2101701481499…, 42471200881885…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 42.19 130.59 9.57 138.18
#3802 [0, -1, 0, -6064909050029…, 41691026783463…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 43.03 133.16 9.80 141.36
#2883 [1, 0, 0, -1305007092705…, 16542549296816…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 43.05 134.43 9.94 143.66
#2876 [0, -1, 0, -4664630695650…, 12261165772114…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 45.38 145.30 11.14 161.30
#2873 [0, -1, 0, -1621105850715…, 49796063311608…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 46.61 150.63 11.24 158.13
#2880 [0, -1, 0, -3319999641863…, 23276122948316…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 47.43 138.60 10.52 153.37
#2881 [0, -1, 0, -8438509927949…, 26297336213181…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 47.46 140.30 10.42 149.26
#2874 [1, 0, 0, -1412825737585…, 15284155642547…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 49.72 149.44 11.16 157.71
#2041 [1, 1, 1, -2797287263082…, -2695185857636…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 60.46 255.90 20.02 263.38
#2868 [1, 0, 0, -2159034712209…, 86432884712007…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 63.48 268.27 21.06 276.42
#2866 [1, 0, 0, -8118635598111…, 21442171049276…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 70.51 292.79 23.11 301.11
#2865 [1, 1, 1, -5399919480636…, -1175494375650…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 70.63 291.54 23.01 299.89
#3780 [1, 1, 1, -5249460128724, 45027997503075…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 27.50 89.11 6.20 99.48
#3566 [0, -1, 0, -3809890521953…, 28617957065131…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 28.81 96.95 7.08 112.33
#3775 [1, 0, 0, -2327914563508…, 39375606629317…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 29.81 94.73 6.63 103.95
#3777 [1, 0, 0, -6145633054189, 53905649417331…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 29.84 90.63 6.29 99.95
#3474 [1, 1, 1, -3142081556619…, -3379133522064…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 29.95 104.28 7.38 111.76
#3799 [1, 1, 1, -1043438552121…, 12973238863652…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 30.24 89.66 7.07 115.36
#3781 [1, 1, 1, -9381673137660, 21193174754651…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 30.26 93.73 6.50 101.22
#3782 [0, -1, 0, -1136104978644…, 46439742496214…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 30.36 96.33 6.88 108.70
#3797 [1, 1, 1, -5654455725437…, 37098750707353…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 30.57 105.34 7.49 113.52
#3800 [1, 0, 0, -5298697071017…, 14838236724151…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 30.73 105.88 7.77 120.23
#3796 [1, 1, 1, -4568155804364…, 11426988239588…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 31.15 109.75 7.91 119.79
#3760 [0, -1, 0, -1114373849930…, -1089675463152…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 31.18 93.42 6.50 101.74
#3473 [0, -1, 0, -7289132920284…, 59870607570494…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 31.27 105.85 7.53 114.28
#2123 [0, -1, 0, -1295200614248…, 10024622212124…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 31.79 108.18 7.71 116.01
#3783 [1, 0, 0, -3274297371809…, 23590453460664…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 31.81 97.40 6.81 104.97
#3793 [1, 0, 0, -4067685412315…, 99854713518280…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 32.26 99.15 7.53 119.44
#3776 [0, -1, 0, -4852124223781…, 36842222172328…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 32.73 103.99 7.40 113.06
#3778 [0, 1, 0, -9820744948538…, 27076288165007…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 33.25 100.07 7.05 108.27
#3794 [1, 0, 0, -2527654502551…, 15467662148555…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 33.25 99.16 7.87 124.92
#3740 [1, 1, 1, -1607842000383…, 78442984976996…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 33.51 108.89 8.03 123.56
#3784 [1, 1, 1, -6456636025920…, 41243023074393…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 33.58 99.51 6.98 107.01
#3774 [0, -1, 0, -1764644477606…, 88596428717573…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 33.96 99.24 7.06 110.03
#3779 [0, 1, 0, -5810354758938…, 52976567591004…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 34.04 102.77 7.36 113.60
#3795 [1, 1, 1, -2302422481432…, 42523104693927…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 34.21 97.58 7.39 117.73
#1829 [1, 0, 0, -4906764644296…, -1050023235516…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 34.35 119.39 8.64 126.91
#1815 [1, 0, 0, -1142413426785…, 13810425722951…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 36.04 120.00 8.74 129.44
#3521 [0, 1, 0, -4727871213189…, 10333719083064…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 38.13 133.09 9.78 140.61
#1376 [1, 0, 0, -3052093665091…, 20523188508026…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 42.83 172.10 13.74 194.56
#2047 [1, 0, 0, -2078158957197…, -1125593515635…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 46.06 182.90 14.02 193.41
#1763 [0, -1, 0, -1030521694067…, 39883498265835…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 46.39 152.25 11.50 163.67
#2122 [0, 1, 0, -30867739684, 20710921965930…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 21.61 72.45 4.86 84.07
#3591 [0, -1, 0, -55432612640, 50194290424320…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 21.95 71.92 4.92 85.83
#3761 [1, 1, 1, -4813456386275, 39855953346673…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.28 88.51 6.16 99.22
#1684 [0, -1, 0, -12528422340, 53931075412410…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.55 67.50 4.55 81.37
#3586 [0, -1, 0, -30594886944, 16588637950832…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.63 75.55 5.01 84.05
#3749 [1, 0, 0, -1523953644, 20076482101599] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.73 66.13 4.24 75.05
#3737 [0, -1, 0, -1325894564, 12210761491524] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.76 66.61 4.25 74.63
#3752 [1, 0, 0, -3986123229, 56575621948824] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 22.78 70.06 4.54 77.93
#3753 [1, 0, 0, -5924609140, 14266167902697…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.07 70.59 4.60 79.12
#830 [0, -1, 0, -629485902400, 16105355246620…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.17 84.45 5.76 93.12
#3584 [0, 1, 0, -136147648080, 19331747261718…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.21 73.29 5.10 88.52
#3738 [0, -1, 0, -14768521300, -9599263797500] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.54 74.41 4.89 81.86
#3592 [0, -1, 0, -111368911344, 14304536635843…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.75 71.24 5.00 87.92
#3748 [0, -1, 0, -13076969284, 33780383064672…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 23.97 73.62 4.83 81.50
#1694 [1, 0, 0, -6769521299, 12220501508724…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 24.41 71.67 4.67 79.52
#3590 [0, -1, 0, -80087385824, 81920574267248…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 24.46 77.34 5.19 86.93
#3736 [1, 0, 0, -928983058679, -2992827242068…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 24.53 85.43 5.84 94.29
#3728 [0, 1, 0, -127664786100, -2115676130746…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 24.70 80.86 5.43 88.33
#828 [0, -1, 0, -23463936760, 54234820318720…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 24.98 75.63 5.00 83.25
#3750 [0, -1, 0, -17997960580, 80678291898490…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.21 73.60 4.86 82.45
#3729 [0, -1, 0, -61596089360, 16267712532096…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.24 78.61 5.24 86.15
#3585 [0, 1, 0, -349607318480, 79525435374086…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.47 76.97 5.36 91.35
#829 [0, 1, 0, -116635432264, 82692405759397…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.47 80.26 5.39 88.06
#3735 [0, 1, 0, -317516125620, 68847883676337…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.48 75.98 5.31 91.06
#3751 [0, 1, 0, -25158134820, 76255491846960…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 25.74 75.72 5.01 83.46
#3730 [0, -1, 0, -39310504660, -6011888756373…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 26.05 77.30 5.13 84.80
#3580 [0, -1, 0, -7244367045024, 75046661570661…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 26.08 83.57 6.04 100.45
#3583 [0, -1, 0, -680773488120, 21609321002585…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 26.82 78.96 5.53 93.35
#3569 [0, -1, 0, -1022036704280, 39438052152848…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 26.83 83.02 5.74 94.57
#3731 [0, -1, 0, -93491957284, 13471892031360…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 27.00 79.94 5.35 87.40
#3571 [0, -1, 0, -9376814107704, 11013189122859…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 28.84 88.80 6.26 101.22
#2055 [0, 1, 0, -9630104529315…, 11502552305812…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 29.64 108.27 8.31 128.93
#3570 [0, -1, 0, -6277533440224…, 19088190711467…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 30.00 94.32 6.72 106.93
#2780 [1, 0, 0, -1984625901969…, -5573036198135…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 32.86 130.55 9.57 138.01
#2772 [0, -1, 0, -2854146384555…, -3145008298992…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 32.92 131.62 9.66 139.10
#2764 [0, 1, 0, -1838963296359…, 30353340197254…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 33.71 125.14 9.65 144.69
#2763 [1, 0, 0, -1382347325962…, -1977923813713…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 33.78 142.07 10.85 157.65
#2759 [1, 0, 0, -4736527724431…, -1120226559848…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 33.85 152.29 11.42 161.34
#2756 [1, 0, 0, -4973499813219…, 13500026591750…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 33.97 129.82 9.95 147.67
#2751 [0, 1, 0, -2850512488930…, -1841219529265…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 33.98 138.44 10.23 146.00
#2744 [1, 0, 0, -1002656559706…, 38582032060201…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 35.02 136.57 10.27 149.78
#2738 [1, 0, 0, -5432606433627…, 50852129363364…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 35.28 140.37 10.39 147.94
#1115 [0, -1, 0, -37513424, 88448315904] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 13.90 39.85 2.82 63.93
#3354 [0, -1, 0, -875284, 140750404] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 15.47 44.98 2.44 52.66
#3355 [1, 1, 1, -1076354, -86661394] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 15.55 45.79 2.51 53.28
#3744 [0, -1, 0, -50566624, 135581138944] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 15.75 54.17 3.30 64.83
#3743 [0, -1, 0, -21263320, 36967992832] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 15.76 51.58 3.08 62.23
#3741 [1, 1, 1, -32658455, 71822257652] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 15.88 42.35 2.85 63.52
#3746 [0, -1, 0, -41899844, 104399119044] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 16.22 47.86 3.04 64.27
#2172 [0, -1, 0, -10428240, 9127296000] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 16.51 51.95 3.04 60.09
#3742 [0, -1, 0, -16708144, 17923062784] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 16.99 53.43 3.16 61.51
#3747 [0, 1, 0, -39905320, 96935961668] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 17.20 50.23 3.11 64.12
#3745 [0, 1, 0, -13097864, 14682820356] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 17.36 52.28 3.07 60.78
#2061 [1, 0, 0, -3072505791404, 17006233003330…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.32 89.30 6.16 97.87
#2716 [0, -1, 0, -119861866360, 15940291844569…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.33 75.17 5.14 88.14
#2060 [1, 1, 1, -125088518240, -2591233519185…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.47 80.79 5.42 88.27
#2710 [1, 0, 0, -3971207861040, 27858455652526…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.60 89.38 6.19 98.64
#2706 [0, -1, 0, -153949014520, -2265430123727…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.64 78.45 5.32 88.89
#2699 [1, 1, 1, -1793790311830, 86979237000028…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.71 86.64 5.97 96.26
#2694 [1, 0, 0, -1047851267396…, 13045978923941…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.94 87.58 6.23 101.55
#2688 [1, 0, 0, -1242562543394…, -7123618758722…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 21.27 108.23 7.71 115.88
#2685 [1, 0, 0, -1867502265314, 87898661130004…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 21.61 87.31 6.01 96.38
#2682 [1, 0, 0, -3099197884060, 20998910752691…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 21.68 81.39 5.84 97.90
#2062 [1, 0, 0, -1957385103361…, 11455664232096…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 27.56 137.30 10.13 144.88