kummer-notes-code

Notes and code from my early research in Kummer Theory for Elliptic Curves.
git clone https://git.tronto.net/kummer-notes-code
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1k-max3-posrank.sage (31759B)


      1 
      2 # Elliptic curves downloaded from the LMFDB downloaded on 30 January 2019.
      3 # Below is a list called data. Each entry has the form:
      4 #   [a1,a2,a3,a4,a6] (Weierstrass Coefficients)
      5 
      6 
      7 data = [\
      8 [1,1,0,-82,-305],\
      9 [0,0,1,-1,0],\
     10 [0,0,0,1,6],\
     11 [0,1,0,0,4],\
     12 [1,1,1,-55,134],\
     13 [1,1,0,-6,4],\
     14 [1,0,1,1,0],\
     15 [1,1,0,1,1],\
     16 [1,1,0,-7,5],\
     17 [1,0,0,-1,2],\
     18 [1,-1,1,-2,0],\
     19 [0,1,1,-1,-1],\
     20 [0,-1,1,-1,-2],\
     21 [0,0,1,-3,0],\
     22 [0,0,1,-3,2],\
     23 [0,-1,1,2,-2],\
     24 [0,1,1,-12,2],\
     25 [0,1,0,0,1],\
     26 [0,1,0,2,0],\
     27 [1,1,0,3,-3],\
     28 [0,0,0,-1,1],\
     29 [0,-1,0,16,0],\
     30 [0,0,0,1,-1],\
     31 [0,-1,1,-19,39],\
     32 [0,-1,0,4,-8],\
     33 [1,1,1,-102,355],\
     34 [1,1,0,7,-9],\
     35 [0,1,1,-441,3422],\
     36 [1,0,0,-7,9],\
     37 [0,0,1,-21,40],\
     38 [0,0,0,-412,3316],\
     39 [0,-1,0,-9,13],\
     40 [0,1,0,-57,171],\
     41 [1,-1,1,25,-26],\
     42 [0,-1,0,3,-11],\
     43 [0,-1,0,3,-2],\
     44 [1,-1,0,13,-11],\
     45 [0,0,0,-7,-2],\
     46 [1,1,1,-39,-35],\
     47 [0,-1,1,19,100],\
     48 [1,-1,1,-7,8],\
     49 [1,0,1,-15,22],\
     50 [1,1,0,-33,61],\
     51 [1,-1,0,-15,-46],\
     52 [1,-1,0,-19,37],\
     53 [0,1,0,11,695],\
     54 [1,0,1,-7,14],\
     55 [0,1,0,3,11],\
     56 [1,0,1,-2,1],\
     57 [1,-1,1,-2,28],\
     58 [0,1,0,0,-1],\
     59 [0,0,1,-12,4],\
     60 [1,-1,0,21,53],\
     61 [1,-1,0,-935,11229],\
     62 [1,1,0,-2819,-58803],\
     63 [1,1,1,-784,8720],\
     64 [0,0,0,1,1],\
     65 [0,0,0,-8,16],\
     66 [1,1,1,-8,9],\
     67 [1,-1,0,12,-208],\
     68 [0,-1,0,-383,3012],\
     69 [0,1,0,6,-43],\
     70 [1,1,0,81,-27],\
     71 [0,-1,0,-10,17],\
     72 [0,1,1,1815,141239],\
     73 [1,-1,0,-2,1],\
     74 [1,-1,0,-4,-2],\
     75 [0,0,0,-6,5],\
     76 [1,-1,0,-18,36],\
     77 [0,-1,0,-13,25],\
     78 [0,-1,0,-12,24],\
     79 [0,-1,0,-80,304],\
     80 [0,0,0,-2,4],\
     81 [1,-1,1,8,-5],\
     82 [1,1,1,-9,7],\
     83 [0,-1,0,-544,-4352],\
     84 [1,-1,0,90,436],\
     85 [0,0,1,1,-8],\
     86 [1,1,1,-120,42282],\
     87 [1,1,1,9,13],\
     88 [1,0,0,-185,1401],\
     89 [0,1,1,-4,-2],\
     90 [1,1,1,-17,-70],\
     91 [0,0,0,2,1],\
     92 [1,1,0,-12,12],\
     93 [1,1,1,-18,415],\
     94 [0,-1,0,4,-3],\
     95 [1,-1,1,-374,2949],\
     96 [1,-1,1,-171,1904],\
     97 [1,-1,0,-1414,-44027],\
     98 [1,-1,1,-12,18],\
     99 [0,1,1,-1006,11952],\
    100 [0,0,1,-111,450],\
    101 [1,-1,0,0,2],\
    102 [0,1,0,-233,1563],\
    103 [0,0,0,-8,9],\
    104 [0,0,1,43,-2088],\
    105 [1,1,0,-1,-2],\
    106 [0,1,1,9,344],\
    107 [1,0,1,-1,1],\
    108 [0,0,0,-27,27],\
    109 [1,-1,1,2064,18771],\
    110 [0,1,1,-16649,821406],\
    111 [0,1,0,-11,11],\
    112 [0,0,1,-4,-3],\
    113 [1,0,1,-10758,428760],\
    114 [1,0,1,1,1],\
    115 [0,0,1,-12,9],\
    116 [0,0,1,242,-333],\
    117 [1,0,1,-722,7396],\
    118 [1,0,1,706,-64375],\
    119 [1,0,1,-17,56],\
    120 [1,0,1,31,20],\
    121 [1,-1,0,-3,-1],\
    122 [1,-1,0,-2430,46732],\
    123 [0,0,0,1468,-2844],\
    124 [1,-1,1,-11,27],\
    125 [1,0,1,6,1],\
    126 [0,1,0,1,2],\
    127 [0,-1,1,-2,2],\
    128 [0,-1,0,-4,5],\
    129 [0,0,0,-67,226],\
    130 [1,1,0,-59,-201],\
    131 [1,-1,0,-70,244],\
    132 [0,1,0,-1,1],\
    133 [0,0,1,-5,4],\
    134 [0,1,1,0,2],\
    135 [1,1,0,-512,4237],\
    136 [0,-1,1,1,-1],\
    137 [1,0,0,31,-192],\
    138 [0,0,1,-75,256],\
    139 [0,1,0,-1,31],\
    140 [0,-1,1,-4,-2],\
    141 [0,1,1,-10,10],\
    142 [1,0,1,2,0],\
    143 [0,-1,0,-432,-3316],\
    144 [1,1,1,2,-1],\
    145 [0,-1,1,-83,3818],\
    146 [1,0,1,-3,0],\
    147 [0,1,0,84,36],\
    148 [0,1,1,-156,700],\
    149 [1,1,1,-56,-135],\
    150 [0,-1,0,-1,2],\
    151 [0,-1,1,2,0],\
    152 [0,-1,1,1,0],\
    153 [1,1,1,13,177],\
    154 [1,0,0,-19,33],\
    155 [1,-1,0,-1,1],\
    156 [1,0,0,-5,4],\
    157 [0,0,1,-3,4],\
    158 [0,-1,0,8,-4],\
    159 [0,1,0,-3,-2],\
    160 [0,1,0,1,1],\
    161 [1,0,0,-1,0],\
    162 [0,0,0,-12,20],\
    163 [0,0,0,-2,0],\
    164 [1,0,0,-12,16],\
    165 [1,1,0,2,1],\
    166 [1,-1,1,0,0],\
    167 [0,-1,1,10,6],\
    168 [1,-1,0,-80,-256],\
    169 [0,-1,0,-16,29],\
    170 [1,0,0,-6,9],\
    171 [1,0,0,1,25],\
    172 [0,0,0,-584,5444],\
    173 [1,-1,0,1,-1],\
    174 [0,-1,1,-5,6],\
    175 [1,1,0,-794,8289],\
    176 [1,-1,0,1,1],\
    177 [1,0,0,-2,1],\
    178 [1,-1,0,12,35],\
    179 [1,0,0,-6,4],\
    180 [0,0,0,-55,157],\
    181 [1,0,0,-3,2],\
    182 [0,0,1,-81,290],\
    183 [1,1,1,-2,0],\
    184 [0,1,1,-100,406],\
    185 [1,1,0,-30,52],\
    186 [0,-1,0,0,1],\
    187 [1,-1,0,-20,40],\
    188 [0,1,0,-21,31],\
    189 [1,-1,0,0,4],\
    190 [0,0,1,-3,18],\
    191 [0,-1,0,55,93],\
    192 [1,1,1,6,7],\
    193 [0,0,1,-237,1404],\
    194 [1,0,0,-2,-1],\
    195 [1,1,0,2,2],\
    196 [1,1,0,-3,1],\
    197 [0,-1,0,-45,133],\
    198 [1,-1,1,-5,20],\
    199 [1,0,0,-3,-2],\
    200 [0,0,1,-3,-2],\
    201 [0,-1,0,4,4],\
    202 [1,0,1,1,-5],\
    203 [0,1,1,1,1],\
    204 [1,0,0,-213,-1208],\
    205 [1,1,1,-1,0],\
    206 [1,0,1,-23,39],\
    207 [0,1,1,-2376,-61851],\
    208 [0,-1,0,-21,49],\
    209 [1,-1,0,0,1],\
    210 [1,-1,0,-454,5812],\
    211 [1,-1,1,-12,15],\
    212 [0,-1,0,-8,16],\
    213 [0,-1,0,0,4],\
    214 [0,0,1,-9,10],\
    215 [0,1,0,-50,129],\
    216 [1,-1,1,-4,-1],\
    217 [1,0,0,-24,63],\
    218 [1,0,0,0,-1],\
    219 [1,-1,0,-5252,-145223],\
    220 [0,-1,1,-26,68],\
    221 [1,-1,1,-1487,-12905],\
    222 [0,0,0,5,10],\
    223 [1,-1,1,-2,82],\
    224 [0,0,1,-597,8820],\
    225 [0,-1,1,-52,-3863],\
    226 [0,-1,1,-3,2],\
    227 [1,0,0,-3,0],\
    228 [1,1,0,-35,-98],\
    229 [1,-1,0,-5,7],\
    230 [1,-1,1,-149,749],\
    231 [1,0,0,-28,-59],\
    232 [1,-1,1,-117,141],\
    233 [0,1,1,-8,8],\
    234 [0,0,0,-48,196],\
    235 [0,-1,0,2,1],\
    236 [1,1,1,-16,-15],\
    237 [1,1,0,-715,7069],\
    238 [0,-1,0,-1,197],\
    239 [0,1,0,-16,16],\
    240 [1,-1,1,-83,595],\
    241 [0,1,1,-2,-2],\
    242 [1,0,0,43,-31],\
    243 [1,1,1,79,335],\
    244 [1,-1,1,13,-12],\
    245 [1,-1,0,-29,-635],\
    246 [1,-1,0,-2846,59156],\
    247 [1,0,0,-350,2500],\
    248 [1,-1,0,1,-3],\
    249 [1,0,1,-80,-275],\
    250 [1,1,1,4,-1443],\
    251 [0,0,1,3,-4],\
    252 [1,0,1,-8,7],\
    253 [1,1,1,-5,11],\
    254 [1,0,1,-174,880],\
    255 [1,1,1,-3,0],\
    256 [1,-1,1,-61,197],\
    257 [1,-1,0,16,-10],\
    258 [0,-1,0,-3,4],\
    259 [0,1,0,-17,51],\
    260 [1,-1,1,318,-2367],\
    261 [1,0,1,-604,-5734],\
    262 [0,1,1,-11,-16],\
    263 [1,1,0,28,157],\
    264 [1,1,0,0,1],\
    265 [1,1,1,66,-5],\
    266 [0,0,0,-13,-18],\
    267 [0,0,1,175,-1344],\
    268 [1,-1,0,-107,454],\
    269 [1,-1,1,-2,-26],\
    270 [1,0,1,-32,-71],\
    271 [1,1,1,64,258],\
    272 [0,0,0,-17,27],\
    273 [1,1,0,-2,-2],\
    274 [0,-1,0,-1,-1],\
    275 [1,1,0,-97,281],\
    276 [0,0,1,-40,48],\
    277 [1,0,1,-44,-150],\
    278 [1,0,1,-9,28],\
    279 [1,0,0,-11,14],\
    280 [1,-1,0,11,-18],\
    281 [1,-1,1,1,-2],\
    282 [1,1,1,-56,1145],\
    283 [0,0,0,5,-6],\
    284 [1,-1,0,-153,4909],\
    285 [0,0,0,-8,4],\
    286 [0,1,0,8,89],\
    287 [1,0,1,0,-1],\
    288 [1,-1,1,22,105],\
    289 [1,1,1,-70,195],\
    290 [1,-1,1,-509,4677],\
    291 [1,-1,0,-9,-19],\
    292 [0,0,0,-4,4],\
    293 [1,-1,0,12,-19],\
    294 [1,-1,1,-9,9],\
    295 [1,-1,0,-9,-14],\
    296 [0,-1,0,-5,1],\
    297 [1,1,1,-12,45],\
    298 [0,-1,1,-7,10],\
    299 [0,1,0,-8,8],\
    300 [1,-1,1,12,87],\
    301 [1,1,1,1,0],\
    302 [0,0,0,5,42],\
    303 [0,-1,0,-4,8],\
    304 [1,1,0,25,-14],\
    305 [1,0,1,33924,-387702],\
    306 [1,0,1,-1,148],\
    307 [1,0,1,-4,-2],\
    308 [0,1,1,-269,1628],\
    309 [1,-1,0,1,5],\
    310 [0,1,1,-16,-66],\
    311 [1,1,0,-1693,26434],\
    312 [0,0,0,4,-4],\
    313 [0,1,0,-4,0],\
    314 [1,-1,0,-42,-127],\
    315 [1,1,0,-108,-432],\
    316 [1,-1,1,7,-7],\
    317 [0,0,1,-4,3],\
    318 [0,0,1,-808,8840],\
    319 [0,0,0,-192,1028],\
    320 [1,-1,0,-45,139],\
    321 [0,1,1,-179,881],\
    322 [0,1,1,0,0],\
    323 [0,0,0,-68,-236],\
    324 [0,-1,0,3,9],\
    325 [0,0,1,-8,-12],\
    326 [1,0,0,-267,1521],\
    327 [1,0,1,11,0],\
    328 [1,0,1,4,2],\
    329 [1,-1,1,-15,87],\
    330 [0,0,0,-56,-4848],\
    331 [0,0,0,-10,12],\
    332 [0,0,0,-5,4],\
    333 [1,1,0,-1,-1],\
    334 [0,0,0,8,4],\
    335 [1,1,1,0,-2],\
    336 [1,1,1,-26,39],\
    337 [1,0,0,-4,-5],\
    338 [0,-1,0,2,-7],\
    339 [0,-1,1,-1,1],\
    340 [0,1,1,-399,-3184],\
    341 [0,0,0,-484,-5324],\
    342 [0,0,1,1,0],\
    343 [0,1,0,-309,1991],\
    344 [1,-1,1,-48,147],\
    345 [1,-1,0,-5,-3],\
    346 [1,-1,0,18,202],\
    347 [0,0,0,-3,14],\
    348 [0,0,1,-2,1],\
    349 [1,0,1,170,-3237],\
    350 [0,-1,0,-23,51],\
    351 [1,0,0,-1,-64],\
    352 [0,1,0,-6,4],\
    353 [0,0,1,-10,12],\
    354 [1,1,0,2,4],\
    355 [1,-1,1,-28,63],\
    356 [0,-1,1,-6,8],\
    357 [0,1,0,160,3188],\
    358 [1,1,1,-5,0],\
    359 [0,1,1,7,2],\
    360 [1,-1,1,-57,222],\
    361 [1,1,0,-3,-9],\
    362 [1,0,0,-42,36],\
    363 [0,-1,1,-1,0],\
    364 [0,-1,0,-16,32],\
    365 [1,0,1,-44,106],\
    366 [0,-1,1,-8,-82],\
    367 [1,1,1,-118,418],\
    368 [0,-1,0,-140,753],\
    369 [1,0,1,-193,1012],\
    370 [0,1,0,-158,-812],\
    371 [1,-1,0,-2,2],\
    372 [0,1,0,-1,3],\
    373 [1,0,1,-48,-130],\
    374 [1,1,1,10,11],\
    375 [0,0,1,2,0],\
    376 [1,-1,0,-9,-54],\
    377 [0,-1,1,-5781,175862],\
    378 [1,1,0,52,-176],\
    379 [1,0,0,-120,576],\
    380 [1,1,0,-27,-59],\
    381 [0,0,0,-13,18],\
    382 [0,1,0,0,-76],\
    383 [1,1,1,-21,27],\
    384 [1,0,0,-36,81],\
    385 [1,0,0,-1415,20617],\
    386 [1,1,1,-861,9267],\
    387 [1,0,0,-247,809],\
    388 [0,-1,0,-6,9],\
    389 [0,0,0,32,-212],\
    390 [1,1,0,-8,6],\
    391 [0,1,0,-5,-1],\
    392 [1,1,1,-230,1251],\
    393 [1,-1,0,-5,6],\
    394 [0,0,0,4,4],\
    395 [1,-1,0,44,496],\
    396 [1,1,1,24,-23],\
    397 [1,1,0,-13,13],\
    398 [0,0,0,-3,34],\
    399 [1,1,0,-75,250],\
    400 [0,1,0,7,7],\
    401 [1,-1,1,0,3],\
    402 [0,1,1,-197,-208],\
    403 [0,0,1,-2,2],\
    404 [0,1,1,-42,110],\
    405 [0,1,1,-2,2],\
    406 [1,1,1,-7,-3],\
    407 [0,1,1,3,7],\
    408 [0,1,0,-2,9],\
    409 [0,-1,0,-1,5],\
    410 [1,1,1,-11,9],\
    411 [1,0,0,-1,9],\
    412 [0,-1,0,-3,3],\
    413 [0,-1,0,-33,85],\
    414 [0,0,0,-7,7],\
    415 [0,0,1,-2,-1],\
    416 [1,1,0,-22,-44],\
    417 [0,-1,1,-5,-16],\
    418 [0,0,1,6,13],\
    419 [0,1,1,-6,2],\
    420 [0,0,1,49,-86],\
    421 [1,1,1,-1001,12375],\
    422 [1,1,1,-21,-5],\
    423 [1,1,0,-2,-12],\
    424 [1,0,0,4,-3],\
    425 [0,1,1,-1,1],\
    426 [0,0,1,-38,90],\
    427 [1,-1,1,1,7],\
    428 [1,1,1,1,2],\
    429 [0,1,1,-310,3364],\
    430 [1,-1,1,-14,-16],\
    431 [1,-1,1,-2,2],\
    432 [0,-1,0,-221,-1191],\
    433 [1,1,1,1,5],\
    434 [1,1,0,-4,2],\
    435 [1,1,1,-539,4592],\
    436 [0,1,0,-5,7],\
    437 [1,1,1,-32,65],\
    438 [1,-1,1,-118,2693],\
    439 [1,-1,1,1,0],\
    440 [0,1,1,2,0],\
    441 [1,-1,1,-5,6],\
    442 [1,1,1,2,0],\
    443 [0,0,0,-48,-124],\
    444 [1,-1,0,-495,-4118],\
    445 [1,0,1,32,-210],\
    446 [0,-1,0,-45,25],\
    447 [1,-1,0,-2,4],\
    448 [1,0,1,-103,-406],\
    449 [0,1,0,8,4],\
    450 [1,-1,0,3,-10],\
    451 [1,1,1,-4,-4],\
    452 [1,-1,1,13,1235],\
    453 [1,-1,0,9,4],\
    454 [1,-1,0,3,0],\
    455 [0,-1,1,-10,16],\
    456 [0,1,0,-1621,24623],\
    457 [1,-1,1,-4,7],\
    458 [0,1,1,10,44],\
    459 [1,-1,0,-24990,1526804],\
    460 [0,0,0,-3,322],\
    461 [1,1,1,-2,15],\
    462 [1,1,1,-14,75],\
    463 [1,-1,1,4,-34],\
    464 [0,0,0,24,16],\
    465 [1,1,1,-4,-3],\
    466 [1,1,1,126,1167],\
    467 [0,1,1,4,14],\
    468 [0,-1,0,11,-47],\
    469 [0,1,0,-15,25],\
    470 [1,0,1,-57,-164],\
    471 [0,0,1,-3,22],\
    472 [0,-1,0,7,-3],\
    473 [1,-1,1,0,2],\
    474 [1,0,1,0,10],\
    475 [0,1,0,3,-9],\
    476 [1,-1,0,66,116],\
    477 [0,-1,0,56,-1415],\
    478 [0,1,1,-1,-4],\
    479 [0,1,0,-61,-205],\
    480 [1,-1,0,-67,216],\
    481 [1,-1,1,-41,105],\
    482 [1,-1,0,135,-243],\
    483 [1,0,1,-5,2],\
    484 [0,-1,0,-61,205],\
    485 [0,-1,0,-20,40],\
    486 [1,-1,1,-248,1563],\
    487 [0,-1,0,-1373,-19191],\
    488 [1,-1,0,-54,-243],\
    489 [0,0,0,-187,991],\
    490 [0,0,0,-5,2],\
    491 [1,0,1,6,-20],\
    492 [1,-1,0,-1773,63909],\
    493 [1,-1,0,8,291],\
    494 [1,-1,1,51,117],\
    495 [0,1,0,-400,-3308],\
    496 [0,1,0,-276,1676],\
    497 [1,1,1,-2460,45949],\
    498 [0,1,1,-33,94],\
    499 [1,-1,0,-117,166],\
    500 [1,0,0,-65,201],\
    501 [0,-1,0,-36,232],\
    502 [1,1,1,-5,3],\
    503 [0,0,0,1,-6],\
    504 [1,0,1,-1,4],\
    505 [0,1,1,79,-214],\
    506 [0,1,0,-4,-8],\
    507 [0,1,0,0,-16],\
    508 [1,0,1,-22,40],\
    509 [1,1,0,1,-1],\
    510 [0,1,0,0,16],\
    511 [1,-1,1,-55,72],\
    512 [0,1,1,-18,24],\
    513 [0,0,1,-1507,4209],\
    514 [0,0,0,-8,-16],\
    515 [0,-1,0,-28,68],\
    516 [1,0,1,-539,4765],\
    517 [1,-1,1,-1,17],\
    518 [1,-1,1,-5,2],\
    519 [0,1,0,-1,51],\
    520 [0,-1,1,23004,2393001],\
    521 [0,0,0,800,26500],\
    522 [0,0,0,5,-2],\
    523 [1,-1,1,-26,57],\
    524 [1,-1,0,0,-3],\
    525 [1,-1,1,-514,4609],\
    526 [0,1,1,-28,48],\
    527 [0,1,0,-9,-13],\
    528 [0,-1,0,-1,17],\
    529 [1,1,0,-2,1],\
    530 [1,1,1,4,-3],\
    531 [1,1,0,13,13],\
    532 [1,1,1,-42,87],\
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