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1
2\\ Elliptic curves downloaded from the LMFDB downloaded on 31 January 2019.
3\\ Below is a list called data. Each entry has the form:
4\\ [a1,a2,a3,a4,a6] (Weierstrass Coefficients)
5
6\\~2000 curves with rank 1 and conductor <1000
7
8data = [\
9[0,0,1,-1,0],\
10[0,1,1,0,0],\
11[1,-1,1,0,0],\
12[0,-1,1,-2,2],\
13[1,-1,0,-1,1],\
14[1,0,0,-2,1],\
15[1,0,0,-1,0],\
16[1,0,0,4,1],\
17[0,0,1,2,0],\
18[1,1,1,-2,0],\
19[1,0,1,-12,-16],\
20[1,0,1,-2,0],\
21[1,1,1,1,0],\
22[0,0,0,-4,4],\
23[1,1,1,-1,0],\
24[0,0,1,1,0],\
25[0,1,1,-117,-1245],\
26[0,1,1,-7,5],\
27[0,1,1,13,42],\
28[0,0,0,-1,1],\
29[1,-1,1,-17,30],\
30[1,-1,1,-2,0],\
31[0,1,1,-1,-1],\
32[1,1,0,-2,0],\
33[1,1,0,8,10],\
34[1,1,0,-7,5],\
35[0,1,0,-40,84],\
36[0,1,0,0,4],\
37[1,-1,1,-626,6180],\
38[1,-1,1,-176,-768],\
39[1,-1,1,-41,96],\
40[1,-1,1,4,6],\
41[1,1,0,1,1],\
42[0,-1,1,-887,-10143],\
43[0,-1,1,-7,10],\
44[1,0,1,2,0],\
45[0,1,1,-10,10],\
46[0,1,1,20,-890],\
47[0,-1,1,1,-1],\
48[0,1,0,-2,1],\
49[0,1,0,18,-11],\
50[0,1,0,-9,7],\
51[0,1,0,1,1],\
52[0,-1,1,-19,39],\
53[1,0,1,-208,-1122],\
54[1,0,1,-33,68],\
55[1,0,1,-13,156],\
56[1,0,1,112,-4194],\
57[0,-1,1,1,0],\
58[0,0,1,-3,4],\
59[0,1,0,-4,0],\
60[0,1,0,16,16],\
61[1,1,0,-31,55],\
62[1,1,0,-1,1],\
63[0,1,1,-12,2],\
64[0,-1,1,-1,0],\
65[1,1,0,-1,-1],\
66[1,-1,1,-12,15],\
67[0,-1,1,-1,-2],\
68[1,-1,1,-3,2],\
69[1,-1,1,2,6],\
70[0,-1,0,-5,1],\
71[0,1,0,-1,3],\
72[0,0,1,-3,2],\
73[0,0,1,-534,4752],\
74[0,0,1,6,27],\
75[1,-1,0,-469,4029],\
76[1,-1,0,-29,69],\
77[0,-1,1,-840,-9114],\
78[0,-1,1,10,6],\
79[0,-1,1,-1,1],\
80[0,-1,0,-20,-24],\
81[0,-1,0,-5,6],\
82[1,1,0,-3,1],\
83[1,-1,1,-9,9],\
84[0,1,0,-6,4],\
85[0,1,0,-1,15],\
86[1,-1,0,-6,8],\
87[1,-1,0,39,-19],\
88[0,0,1,-2,1],\
89[1,1,0,-6,4],\
90[1,0,1,-8,6],\
91[1,0,1,12,38],\
92[0,0,1,-6924,221760],\
93[0,0,1,-84,315],\
94[0,0,1,6,0],\
95[0,1,0,-13,15],\
96[0,1,0,67,79],\
97[0,-1,1,-148,748],\
98[0,-1,1,2,-2],\
99[0,-1,1,-3283,-74657],\
100[0,-1,1,-33,93],\
101[0,-1,1,217,-282],\
102[0,-1,0,-77,289],\
103[0,-1,0,3,1],\
104[0,-1,0,0,1],\
105[0,-1,0,-4,5],\
106[0,1,1,-156,700],\
107[0,-1,1,-5,6],\
108[1,0,1,-4,-3],\
109[1,0,1,1,-9],\
110[0,0,1,-3,0],\
111[0,0,1,-3834,-91375],\
112[0,0,1,-54,-88],\
113[0,0,1,-24,45],\
114[1,1,0,2,2],\
115[1,-1,1,-48,147],\
116[0,-1,0,-129,609],\
117[0,-1,0,-9,9],\
118[0,-1,0,-4,-2],\
119[0,-1,0,31,33],\
120[0,-1,0,-142,701],\
121[0,-1,0,-2,1],\
122[0,0,1,-5,4],\
123[1,-1,0,-3168,69430],\
124[1,-1,0,-198,1120],\
125[1,-1,0,-108,2074],\
126[1,-1,0,-18,4],\
127[0,1,0,-28,48],\
128[0,1,0,-3,-2],\
129[0,-1,1,2,0],\
130[1,0,0,-1,2],\
131[1,1,0,-794,8289],\
132[1,1,1,0,-2],\
133[1,-1,1,-232,-1286],\
134[1,-1,1,-27,26],\
135[1,-1,1,-22,44],\
136[1,-1,1,98,126],\
137[1,-1,1,-140,668],\
138[1,-1,1,-5,20],\
139[0,-1,0,-7352,245104],\
140[0,-1,0,-72,496],\
141[0,-1,0,8,-16],\
142[0,-1,0,-16,32],\
143[0,1,1,-27,55],\
144[0,1,1,193,-308],\
145[1,1,0,-373,2623],\
146[1,1,0,-23,33],\
147[1,1,0,-3,-3],\
148[1,1,0,7,147],\
149[0,-1,0,-4,8],\
150[1,0,1,1,0],\
151[1,0,1,-193,1012],\
152[1,0,0,-12,16],\
153[0,0,1,-8,-12],\
154[0,0,0,-12,20],\
155[1,0,0,-2,4],\
156[1,0,0,18,-104],\
157[0,-1,1,-6,8],\
158[0,1,1,-27,-85],\
159[0,1,1,3,2],\
160[1,1,0,-1297,-18530],\
161[1,1,0,-82,-305],\
162[0,1,0,-7100,-232652],\
163[0,1,0,-445,-3720],\
164[0,1,0,-100,-252],\
165[0,1,0,-45,100],\
166[0,1,0,-8,-8],\
167[0,1,0,2,0],\
168[0,0,1,-75,256],\
169[0,0,1,375,-12344],\
170[0,0,1,0,-34],\
171[0,0,1,0,1],\
172[1,0,0,-45,-119],\
173[1,0,0,-5,1],\
174[0,-1,0,3,9],\
175[1,0,0,-2,-1],\
176[0,-1,0,8,-4],\
177[1,-1,0,-63,209],\
178[1,-1,0,-3,5],\
179[1,1,1,-5,0],\
180[0,-1,0,-1,2],\
181[1,-1,0,-8,6],\
182[1,-1,0,2,0],\
183[1,0,0,-700,7056],\
184[1,0,0,-60,16],\
185[0,-1,0,-216,1296],\
186[0,-1,0,-136,-560],\
187[0,-1,0,-16,16],\
188[0,-1,0,4,0],\
189[1,0,0,-52,144],\
190[1,0,0,3,1],\
191[0,0,1,0,-1],\
192[0,0,1,0,20],\
193[0,0,0,1,6],\
194[0,0,1,-7,12],\
195[0,-1,1,-6435,210006],\
196[0,-1,1,-65,-204],\
197[0,-1,1,425,433],\
198[1,1,0,-66,180],\
199[1,1,0,-26,444],\
200[0,1,0,0,1],\
201[0,0,0,1,-1],\
202[1,1,1,-55,134],\
203[1,1,0,2,1],\
204[0,0,0,-327,2270],\
205[0,0,0,-12,65],\
206[1,-1,0,-5,-3],\
207[1,0,0,-24432,-1471934],\
208[1,0,0,-302,-2036],\
209[1,0,0,-22,36],\
210[0,1,0,-13,-21],\
211[0,1,0,-3,1],\
212[0,0,0,-2,0],\
213[0,0,0,8,0],\
214[1,1,0,3,-3],\
215[1,0,1,-15,22],\
216[1,-1,0,-2,2],\
217[1,0,0,1,25],\
218[1,-1,1,-138,656],\
219[1,-1,1,-133,702],\
220[0,0,1,-2,-1],\
221[0,1,0,-48,-140],\
222[0,1,0,-8,4],\
223[0,0,0,-1451,21274],\
224[0,0,0,-91,330],\
225[0,0,0,-11,-6],\
226[0,0,0,-11,890],\
227[0,-1,1,-26,68],\
228[1,-1,0,-2846,59156],\
229[1,-1,0,-2,0],\
230[1,-1,0,8,-6],\
231[1,0,0,-7,9],\
232[1,-1,1,-1480,22272],\
233[1,-1,1,-730,-7228],\
234[1,-1,1,-105,272],\
235[1,-1,1,20,22],\
236[1,0,1,0,-1],\
237[1,0,0,-1,9],\
238[0,0,0,-412,3316],\
239[0,-1,0,-1,5],\
240[1,1,1,-255,1461],\
241[1,1,1,-15,21],\
242[1,0,0,-76,-19],\
243[1,0,0,19,0],\
244[1,1,0,-93,-378],\
245[1,1,0,2,-17],\
246[1,1,0,-33,61],\
247[1,1,1,13,177],\
248[0,0,0,-12,0],\
249[0,0,0,3,0],\
250[0,0,0,-291,-1910],\
251[0,0,0,-156,736],\
252[0,0,0,-21,-20],\
253[0,0,0,69,-146],\
254[1,-1,1,-26209,-1626560],\
255[1,-1,1,-1644,-24922],\
256[1,-1,1,-199,-68272],\
257[1,-1,1,-199,510],\
258[1,-1,0,-70,-204],\
259[1,-1,0,10,-700],\
260[1,1,1,-18,-36],\
261[1,1,1,-3,0],\
262[1,0,1,-138,592],\
263[1,0,1,2,32],\
264[0,-1,0,-9,13],\
265[0,-1,0,-33,85],\
266[0,0,1,-81,290],\
267[1,-1,1,1,0],\
268[1,-1,0,12,-19],\
269[1,-1,0,1,-1],\
270[1,0,0,-19,33],\
271[0,-1,0,-13,22],\
272[0,-1,0,12,72],\
273[1,-1,1,0,3],\
274[1,1,1,-230,1251],\
275[1,1,1,1650,-27389],\
276[0,1,1,-6,2],\
277[0,1,1,-197,-208],\
278[0,1,0,-21,31],\
279[0,-1,0,-8,16],\
280[0,1,0,-1120,15604],\
281[0,1,0,0,-76],\
282[1,-1,0,-1017,8883],\
283[1,-1,0,-927,11097],\
284[1,-1,0,-387,-2835],\
285[1,-1,0,-27,-27],\
286[0,-1,0,-21,49],\
287[1,0,0,-6,9],\
288[1,0,0,-2046,15376],\
289[1,0,0,-1706,26980],\
290[1,0,0,-106,420],\
291[1,0,0,454,1876],\
292[0,-1,0,-3,0],\
293[0,-1,0,12,-12],\
294[0,1,0,-60,144],\
295[0,1,0,5,14],\
296[1,-1,0,13,-11],\
297[1,-1,1,-1013,12656],\
298[1,-1,1,-68,182],\
299[1,-1,1,-23,-34],\
300[1,-1,1,157,992],\
301[0,0,0,-7,-2],\
302[1,1,0,7,-9],\
303[1,1,1,-12,45],\
304[0,1,0,-165,763],\
305[0,1,0,-145,975],\
306[0,1,0,-5,-5],\
307[0,1,0,15,-17],\
308[0,0,0,-428,-3408],\
309[0,0,0,-28,-48],\
310[0,0,0,-8,8],\
311[0,0,0,52,-272],\
312[1,-1,0,-238,1470],\
313[1,-1,0,-8,44],\
314[1,0,0,-174,868],\
315[1,0,0,-14,4],\
316[0,0,0,-189,-999],\
317[0,0,0,-9,9],\
318[0,-1,1,-53,-132],\
319[0,-1,1,-3,3],\
320[0,1,1,-1333,-19131],\
321[0,1,1,-83,244],\
322[1,-1,0,-80,-256],\
323[1,0,0,-6,4],\
324[1,0,0,4,-3],\
325[0,0,0,-11,-10],\
326[0,0,0,29,-66],\
327[1,1,0,-1602,24024],\
328[1,1,0,-102,324],\
329[1,1,0,-22,-44],\
330[1,1,0,118,1776],\
331[1,0,0,-5,4],\
332[1,-1,1,-14,-14],\
333[1,-1,1,1,-2],\
334[0,0,1,-16860,842625],\
335[0,0,1,-210,1134],\
336[0,0,1,-30,-63],\
337[1,-1,0,-123,494],\
338[1,-1,0,12,35],\
339[0,0,1,-2,2],\
340[0,-1,0,-12544,544960],\
341[0,-1,0,-784,8704],\
342[0,-1,0,-624,-5760],\
343[0,-1,0,-544,13888],\
344[0,-1,0,-64,64],\
345[0,-1,0,16,0],\
346[1,-1,0,-35944,-2868878],\
347[1,-1,0,-454,5812],\
348[1,-1,0,-389,-2859],\
349[1,-1,0,1,1],\
350[1,1,1,-322,2127],\
351[1,1,1,3,-5],\
352[0,1,1,-2,2],\
353[0,1,1,-441,3422],\
354[0,0,0,-28,57],\
355[0,0,0,-23,78],\
356[1,-1,0,-33,-65],\
357[1,-1,0,-3,1],\
358[1,-1,0,-3852,92988],\
359[1,-1,0,-3762,97470],\
360[1,-1,0,-72,0],\
361[1,-1,0,288,-216],\
362[0,0,0,4,4],\
363[0,1,1,-100,406],\
364[0,1,1,-1,1],\
365[1,1,1,-7,-3],\
366[0,1,1,2,0],\
367[0,-1,0,2,1],\
368[0,1,0,-50,129],\
369[1,1,0,-45,-185],\
370[1,1,0,5,5],\
371[1,-1,1,-180,1047],\
372[0,0,0,8,112],\
373[0,-1,0,3,-11],\
374[0,-1,0,-45,133],\
375[0,1,0,3,11],\
376[1,1,0,-715,7069],\
377[1,1,1,-5,11],\
378[0,-1,0,4,-8],\
379[0,1,1,-42,110],\
380[0,-1,1,-5,-16],\
381[1,-1,1,-7,8],\
382[1,0,1,-23,39],\
383[0,0,0,-963,11502],\
384[0,0,0,-63,162],\
385[0,0,0,-18,-27],\
386[0,0,0,117,918],\
387[0,0,1,-13718,-619025],\
388[0,0,1,-38,90],\
389[1,1,0,-4,2],\
390[1,1,1,6,7],\
391[0,1,0,-5,7],\
392[0,0,0,-584,5444],\
393[1,0,1,-5,20],\
394[1,0,1,40,-538],\
395[1,1,1,-32,65],\
396[0,0,0,-55,157],\
397[0,-1,0,-18,43],\
398[0,-1,0,2,-1],\
399[0,0,0,-35,-62],\
400[0,0,0,5,-6],\
401[0,1,0,0,-1],\
402[0,0,1,6,13],\
403[1,-1,0,-395,-2925],\
404[1,-1,0,-25,-39],\
405[1,-1,0,-5,5],\
406[1,-1,0,25,-209],\
407[1,1,0,-35,-98],\
408[0,-1,0,-6,9],\
409[0,1,0,-2,9],\
410[0,1,1,-2,-2],\
411[1,-1,0,-32,0],\
412[1,-1,0,128,-96],\
413[1,-1,0,-158,-725],\
414[1,-1,0,-13,0],\
415[1,-1,0,-8,11],\
416[1,-1,0,52,-39],\
417[1,-1,0,-141,681],\
418[1,-1,0,-96,1088],\
419[1,-1,0,849,-25939],\
420[1,-1,0,0,4],\
421[0,0,0,-103,-402],\
422[0,0,0,-8,-3],\
423[0,1,1,-11,-16],\
424[0,-1,0,-3,3],\
425[0,-1,0,7,9],\
426[0,1,0,-35,69],\
427[0,1,0,-25,119],\
428[1,0,0,-55,150],\
429[1,0,0,0,7],\
430[1,-1,1,-10267,402966],\
431[1,-1,1,-697,5294],\
432[1,-1,1,-642,6416],\
433[1,-1,1,-37,124],\
434[1,-1,1,-2,2],\
435[1,-1,0,-15,-46],\
436[1,1,0,-483,-4293],\
437[1,1,0,-33,-63],\
438[1,1,0,-13,13],\
439[1,1,0,97,-297],\
440[0,0,0,-7,7],\
441[0,-1,0,-16,29],\
442[0,0,0,-14651,-682570],\
443[0,0,0,-2891,47334],\
444[0,0,0,-931,-10290],\
445[0,0,0,49,-686],\
446[0,0,0,-111,214],\
447[0,0,0,24,25],\
448[1,1,1,-48,90],\
449[1,1,1,-13,-22],\
450[1,1,0,-1925,31458],\
451[1,1,0,-210,-441],\
452[0,0,0,5,10],\
453[0,-1,0,-2008,35312],\
454[0,-1,0,-1208,-19088],\
455[0,-1,0,-8,112],\
456[0,-1,0,8792,140912],\
457[0,0,0,-2675,53250],\
458[0,0,0,-175,750],\
459[0,0,0,-50,-125],\
460[0,0,0,325,4250],\
461[1,1,0,-2,-12],\
462[1,0,1,-10255,-438718],\
463[1,0,1,-145,692],\
464[1,0,1,800,1070],\
465[0,0,0,-8,4],\
466[0,0,1,-3,-2],\
467[1,-1,1,-2027,35776],\
468[1,-1,1,-2,-26],\
469[0,0,1,-108,-412],\
470[0,0,1,-18,29],\
471[1,-1,0,-225,-1250],\
472[1,-1,0,0,1],\
473[1,-1,0,-4942,134964],\
474[1,-1,0,-302,2260],\
475[1,0,1,-15,210],\
476[1,0,1,130,-5648],\
477[1,1,1,-102,355],\
478[0,1,0,-17,51],\
479[1,-1,0,-214,1260],\
480[1,-1,0,-14,20],\
481[1,0,0,-16,0],\
482[1,0,0,64,16],\
483[1,-1,0,-2223,-39785],\
484[1,-1,0,-963,11371],\
485[1,-1,0,-153,-455],\
486[1,-1,0,27,-59],\
487[1,-1,1,-1532,23455],\
488[1,-1,1,-92,415],\
489[0,-1,0,0,4],\
490[1,1,1,66,-5],\
491[1,-1,0,1,-3],\
492[0,0,1,-9,10],\
493[0,0,1,-237,1404],\
494[0,0,1,-12,4],\
495[1,-1,0,-6768,-212625],\
496[1,-1,0,-558,-891],\
497[1,-1,0,-423,-3240],\
498[1,-1,0,-18,-81],\
499[1,0,0,-213,-1208],\
500[1,0,0,-88,-2583],\
501[1,0,0,-3,2],\
502[1,1,0,-75,250],\
503[1,-1,0,-2267,-40984],\
504[1,-1,0,-142,-609],\
505[1,-1,0,-17,-1734],\
506[1,-1,0,-17,16],\
507[1,1,0,-4606,118420],\
508[1,1,0,-286,1780],\
509[1,0,0,-28,-59],\
510[1,0,1,-8,7],\
511[0,-1,0,3,-2],\
512[1,1,1,-13,8],\
513[1,1,1,2,2],\
514[1,0,0,-6864,218313],\
515[1,0,0,-3009,-61770],\
516[1,0,0,-474,2619],\
517[1,0,0,-429,3384],\
518[1,0,0,-24,63],\
519[1,0,0,1341,18228],\
520[1,-1,0,-20,40],\
521[1,-1,0,16,-10],\
522[1,0,0,-5626,-162894],\
523[1,0,0,-36,-440],\
524[1,0,0,4,16],\
525[1,0,0,-1415,20617],\
526[1,0,0,0,-1],\
527[0,0,0,-459,3834],\
528[0,0,0,-219,-1654],\
529[0,0,0,21,26],\
530[0,0,0,-3,34],\
531[0,0,0,0,-4],\
532[0,0,0,0,108],\
533[1,-1,0,-47,133],\
534[1,-1,0,-7,-3],\
535[1,0,0,-139,465],\
536[1,0,0,21,49],\
537[0,-1,1,19,100],\
538[1,1,0,-65,-231],\
539[1,1,0,-5,-3],\
540[1,0,1,-98,362],\
541[1,0,1,-8,2],\
542[1,0,1,-32681,1883180],\
543[1,0,1,-31106,2108972],\
544[1,0,1,-9641,-337876],\
545[1,0,1,-1946,32780],\
546[1,1,1,-1559,-24343],\
547[1,1,1,-99,-399],\
548[1,1,1,-19,17],\
549[1,1,1,81,-1479],\
550[0,0,0,-38,-87],\
551[0,0,0,17,-318],\
552[0,0,0,-23,-38],\
553[0,0,0,2,-3],\
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