John Cremona prepared three files with BSD data about elliptic curves. I typed

 awk '$5==1' allbsd.1-8000 allbsd.8001-12000 allbsd.12001-20000 > rank1

to make the subset of his files that is about curves of rank 1. Then, using Python I ran the following commands:

  f=open(``rank1'').read().split(``\n''); x=[[eval(y.split()[9]),y] for y in f if len(y)>10]; x.sort()
  for z in x[:50]:
      print z[0], z[1]

This resulted in the following output, which says that, assuming correctness of Cremona’s allbsd files, for rank 1 optimal curves of conductor up to 20000, the four smallest regulators (hence heights) are approximately 0.00891432445569, 0.00903868188983, 0.00973986614291, and 0.00996410799991, which correspond to the optimal curves 3990V, 3630Y, 1430K, and 1470L. This is the same thing I send in my computation from 2001, except then I only looked at the data for conductors up to 12000.

0.00891432445569 3990 V  1 [1,1,1,-125615,61201397]     1       1       2310    0.23109953490992895008  4.7588223045716933859   0.89143244556863533937e-2       1
0.00903868188983 3630 Y  1 [1,0,0,-141875,18393057]     1       1       1785    0.35400557724617146994  5.7115426829199770947   0.90386818898339096889e-2       1
0.00973986614291 1430 K  1 [1,-1,1,-3057,133281]        1       1       390     0.67776978196517417482  2.5745409112997787816   0.97398661429109179437e-2       1
0.00996410799991 1470 L  1 [1,1,1,-2990,71147]  1       1       390     0.88588471246845036567  3.4425498706977942997   0.99641079999126058232e-2       1
0.0112775268756  280 B  1 [0,0,0,-412,3316]     1       1       60      1.7288713939579846572   1.1698436165891036927   0.11277526875600686835e-1       1
0.0114310356128 3822 GG  1 [1,0,0,-4923717,4228856001]  1       1       2380    0.19231700741971843384  5.2321504946237686737   0.11431035612822702644e-1       1
0.0115555824173 6510 CC  1 [1,0,0,-13465,839225]        1       1       1155    0.5375938166941290872   7.175102152486185893    0.11555582417285710934e-1       1
0.0118509962179 1518 T  1 [1,0,0,-21736,875072] 1       1       660     0.50457068313817547454  3.9465790699851132558   0.11850996217938577451e-1       1
0.0120687789943 1890 P  1 [1,-1,1,-1517,26709]  1       1       330     1.0434357482304609482   4.1556884952389850943   0.12068778994273784838e-1       1
0.0122529773131 1830 L  1 [1,0,0,-8755,350177]  1       1       520     0.70022594790177803388  4.4615233799061430289   0.12252977313073195616e-1       1
0.0128468084018  350 F  1 [1,-1,1,-180,1047]    1       1       66      1.9197624983313408116   1.627746185543306066    0.1284680840182956997e-1        1
0.0132435005474 6090 BB  1 [1,0,0,-10280,409152]        1       1       660     0.79760412804705836914  6.971626666200441605    0.13243500547355602358e-1       1
0.0134167723091  735 F  1 [0,1,1,-310,3364]     1       1       84      1.2882643756245456697   1.4518853833407302663   0.1341677230909686008e-1        1
0.0136447943354 1806 N  1 [1,0,0,-25757,320049] 1       1       715     0.42637776663439978253  4.1597534084501729382   0.1364479433535728082e-1        1
0.0138351336607 7854 S  1 [1,0,0,-350636,80632464]      1       1       1440    0.35695937328060200041  7.1115561227216595615   0.13835133660705875539e-1       1
0.0154251315385 11730 O  1 [1,0,0,59419,1024262145]     1       1       3780    0.13169790914427038313  7.6789096217637222523   0.15425131538495231387e-1       1.00000000000000000000
0.0157652128495  14910 KK   1 [1,0,0,-28335,999225]     1       1       1320    0.44704006769389497424  9.3029400016647826053   0.15765212849486297078e-1       1
0.0157980969745  14430 QQ   1 [1,0,0,-273635,55620225]  1       1       1456    0.37761112381432780485  8.6858220942849528185   0.15798096974498834336e-1       1.00000000000000000000
0.0158333892356  600 E  1 [0,1,0,-233,1563]     1       1       84      1.6232936554871205389   2.1589881844395931626   0.15833389235563030986e-1       1
0.0162515410815 4620 M  1 [0,1,0,-1964205,1059396975]   1       1       945     0.29330985958943427296  4.504566684936822906    0.16251541081536449256e-1       1.00000000000000000000
0.0163345405553  17490 BB   1 [1,0,0,-1588010,774750372]        1       1       2310    0.2540919007225576385   9.5875959959639696061   0.16334540555305432857e-1   1.0000000000000000012
0.0166374352509 7098 FF  1 [1,0,0,-46381,4157009]       1       1       858     0.47825509653854030254  6.8270529773819283998   0.16637435250908252138e-1       1
0.0167027901704 2370 O  1 [1,0,0,-2255,44025]   1       1       280     1.0323246014331322338   4.8279563375336662811   0.16702790170398024602e-1       1
0.0170027905533 7770 DD  1 [1,0,0,-1750,318500] 1       1       840     0.52889471446323561133  7.5538562860081489464   0.17002790553310971099e-1       1
0.0173714666597 2970 DD  1 [1,-1,1,-372332,-54226961]   1       1       1365    0.19894832580841187947  4.7174730449846813211   0.17371466659680026481e-1       1
0.0174159649173 3930 F  1 [1,0,0,-28565,1872225]        1       1       504     0.6715221347130090995   5.8943837934379816897   0.17415964917313259132e-1       1.00000000000000000000
0.0174682919263 1302 M  1 [1,0,0,-1252,18704]   1       1       182     1.1506026777155425792   3.6580295507205063479   0.17468291926282369467e-1       1
0.0184736827364  975 I  1 [0,1,1,-4758,128144]  1       1       84      0.94863094452940498496  1.4720753966665882494   0.18473682736406298279e-1       1
0.0185237308473  430 D  1 [1,0,0,-1415,20617]   1       1       75      1.3842895617477883861   1.92316554424202073     0.18523730847312548364e-1       1.00000000000000000000
0.0188330248451 7350 ZZZ  1 [1,0,0,-2213,146817]        1       1       594     0.63050602855225368344  7.0533554062309328487   0.1883302484512466681e-1        1

0.0188535339486 2550 FF  1 [1,0,0,-1938,25092]  1       1       273     0.94803369856612801525  4.8795434470426984544   0.188535339485679453e-1 1
0.0191397373282 1110 M  1 [1,0,0,-281,2361]     1       1       126     1.4588941518522167657   3.5182792078765042199   0.19139737328243991884e-1       1
0.0192477773539 1020 H  1 [0,1,0,-170,6225]     1       1       135     1.0311221246729365197   2.6793192258473869176   0.19247777353867040001e-1       1
0.0196779110608 4998 II  1 [1,0,0,4409,496649]  1       1       702     0.43742902444997005139  6.0425979858481171829   0.19677911060779567306e-1       1
0.0197560590057  19950 ZZZ   1 [1,0,0,2031662,8219116292]       1       1       5460    0.88751305713947095572e-1       9.5734331375622476079   0.19756059005732673208e-1    0.99999999999999999687
0.0198380094718 2090 O  1 [1,1,1,-3345,74095]   1       1       168     1.1032029171452321554   3.6767387864969967468   0.19838009471782301099e-1       1.00000000000000000000
0.0202709581589  17850 III   1 [1,0,0,-7438,421892]     1       1       780     0.57437229854195597274  9.0815999284612533364   0.20270958158874532536e-1       1.0000000000000000006
0.0204000948681 7350 HHH  1 [1,0,0,-15338,1952292]      1       1       840     0.41988649354083560695  7.1952084137398485011   0.2040009486811034554e-1        1
0.0205680114567  190 A  1 [1,-1,1,-48,147]      1       1       22      2.7276120737371510762   1.2342342404077727975   0.20568011456741253035e-1       1
0.0207213852547 2040 Q  1 [0,1,0,-2840,81813]   1       1       210     0.78718172805606131971  3.4254141290275838654   0.2072138525470275641e-1        1
0.0209484131629 1770 G  1 [1,0,0,-721,15401]    1       1       208     0.96722218201890535126  4.2144481369547531342   0.20948413162850215531e-1       1
0.0209841213184  494 D  1 [1,1,1,-1001,12375]   1       1       78      1.3176510859323960851   2.1566805189122614028   0.20984121318352936515e-1       1
0.0213990182956 6222 E  1 [1,0,0,-265965,212681169]     1       1       1680    0.18638522143347250274  6.7006140826661770692   0.21399018295639899734e-1       1
0.0214001480068  550 I  1 [1,1,1,-2213,39531]   1       1       84      1.2639033911075527953   2.2720084494268717103   0.21400148006828586228e-1       1.00000000000000000000
0.021448892363  345 F  1 [0,1,1,-100,406]       1       1       24      2.0934610738452118798   1.0776581097354627117   0.21448892362971945433e-1       1
0.0215541166685 3450 BB  1 [1,0,0,-2163,24417]  1       1       288     0.87366006584511654692  5.4233196444982932959   0.21554116668507167619e-1       1
0.0218747424901 6468 T  1 [0,1,0,-22682,1438569]        1       1       330     0.55969098415113782598  4.0402217302774912191   0.21874742490134400617e-1       1
0.022332352336 1590 S  1 [1,0,0,-406,3620]      1       1       126     1.4482385313657895336   4.0751642167822866284   0.22332352336023316415e-1       1
0.0224686032667  618 F  1 [1,0,0,-185,1401]     1       1       77      1.5379775186464285799   2.660827915863161338    0.22468603266668315834e-1       1
0.0227175485369 7770 CC  1 [1,0,0,-281490,80204292]     1       1       1300    0.25155767343026346342  7.4292057527615540394   0.22717548536855383737e-1       1