cm-rank+-all.sage - kummer-notes-code - Notes and code from my early research in Kummer Theory for Elliptic Curves.

cm-rank+-all.sage (80229B)
      1 
      2 # Elliptic curves downloaded from the LMFDB downloaded on 23 October 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 [0, -1, 1, -887, -10143],\
      9 [0, -1, 1, -7, 10],\
     10 [0, 0, 1, 0, -34],\
     11 [0, 0, 1, 0, 1],\
     12 [0, 0, 1, 0, -1],\
     13 [0, 0, 1, 0, 20],\
     14 [0, 1, 0, -13, -21],\
     15 [0, 1, 0, -3, 1],\
     16 [0, 0, 0, -2, 0],\
     17 [0, 0, 0, 8, 0],\
     18 [0, 0, 0, -12, 0],\
     19 [0, 0, 0, 3, 0],\
     20 [0, 0, 1, -13718, -619025],\
     21 [0, 0, 1, -38, 90],\
     22 [0, 0, 0, 0, -4],\
     23 [0, 0, 0, 0, 108],\
     24 [1, -1, 1, -16400, -804212],\
     25 [1, -1, 1, -965, -13940],\
     26 [1, -1, 1, -335, 2440],\
     27 [1, -1, 1, -20, 46],\
     28 [0, 0, 1, 0, -331],\
     29 [0, 0, 1, 0, 12],\
     30 [0, 0, 0, -396, -3024],\
     31 [0, 0, 0, -396, 3024],\
     32 [0, 0, 0, -36, 0],\
     33 [0, 0, 0, 9, 0],\
     34 [0, 0, 0, -540, -4752],\
     35 [0, 0, 0, -60, 176],\
     36 [0, 0, 0, 0, -216],\
     37 [0, 0, 0, 0, 8],\
     38 [0, 0, 1, -6750, -213469],\
     39 [0, 0, 1, -750, 7906],\
     40 [0, 0, 1, 0, -844],\
     41 [0, 0, 1, 0, 31],\
     42 [0, 0, 0, -29155, -1915998],\
     43 [0, 0, 0, -1715, -33614],\
     44 [0, 0, 0, -595, 5586],\
     45 [0, 0, 0, -35, 98],\
     46 [0, 0, 0, -275, -1750],\
     47 [0, 0, 0, -275, 1750],\
     48 [0, 0, 0, -25, 0],\
     49 [0, 0, 0, 100, 0],\
     50 [0, 0, 0, -5, 0],\
     51 [0, 0, 0, 20, 0],\
     52 [0, 0, 0, 0, -2700],\
     53 [0, 0, 0, 0, 100],\
     54 [0, 0, 0, 0, -972],\
     55 [0, 0, 0, 0, 36],\
     56 [0, 0, 0, 0, -243],\
     57 [0, 0, 0, 0, 9],\
     58 [0, 0, 1, 0, -2],\
     59 [0, 0, 1, 0, 47],\
     60 [0, 0, 1, 0, -16207],\
     61 [0, 0, 1, 0, 600],\
     62 [0, 0, 1, 0, -192787],\
     63 [0, 0, 1, 0, 7140],\
     64 [0, 0, 1, 0, -88],\
     65 [0, 0, 1, 0, 3],\
     66 [0, 0, 0, -539, -4802],\
     67 [0, 0, 0, -539, 4802],\
     68 [0, 0, 0, -49, 0],\
     69 [0, 0, 0, 196, 0],\
     70 [0, 0, 0, -500, 0],\
     71 [0, 0, 0, 125, 0],\
     72 [0, 0, 0, -20, 0],\
     73 [0, 0, 0, 5, 0],\
     74 [0, 0, 0, -1080, -13662],\
     75 [0, 0, 0, -120, 506],\
     76 [0, 0, 0, 0, -54],\
     77 [0, 0, 0, 0, 2],\
     78 [0, 0, 0, -1080, 13662],\
     79 [0, 0, 0, -120, -506],\
     80 [0, 0, 0, 0, -2],\
     81 [0, 0, 0, 0, 54],\
     82 [0, 0, 0, 0, -28],\
     83 [0, 0, 0, 0, 756],\
     84 [0, 0, 0, -6615, 203742],\
     85 [0, 0, 0, -735, -7546],\
     86 [0, 0, 0, 0, -343],\
     87 [0, 0, 0, 0, 9261],\
     88 [0, 0, 1, -1590140, -771794326],\
     89 [0, 0, 1, -860, 9707],\
     90 [0, 0, 0, -72, 0],\
     91 [0, 0, 0, 18, 0],\
     92 [0, 0, 0, -6, 0],\
     93 [0, 0, 0, 24, 0],\
     94 [0, 0, 0, -120, -448],\
     95 [0, 0, 0, -30, 56],\
     96 [0, 0, 0, -54, 0],\
     97 [0, 0, 0, 216, 0],\
     98 [0, 0, 0, 0, -13500],\
     99 [0, 0, 0, 0, 500],\
    100 [0, 0, 0, 0, -16875],\
    101 [0, 0, 0, 0, 625],\
    102 [0, 0, 0, 0, -135],\
    103 [0, 0, 0, 0, 5],\
    104 [0, 1, 1, -22183, -1312206],\
    105 [0, 1, 1, -183, 919],\
    106 [0, 0, 0, -7, 0],\
    107 [0, 0, 0, 28, 0],\
    108 [0, 0, 0, -2156, -38416],\
    109 [0, 0, 0, -2156, 38416],\
    110 [0, 0, 0, -196, 0],\
    111 [0, 0, 0, 49, 0],\
    112 [0, 0, 0, -116620, -15327984],\
    113 [0, 0, 0, -6860, -268912],\
    114 [0, 0, 0, -2380, 44688],\
    115 [0, 0, 0, -140, 784],\
    116 [0, 0, 0, -343, 0],\
    117 [0, 0, 0, 1372, 0],\
    118 [0, 0, 1, -32670, 2273015],\
    119 [0, 0, 1, -3630, -84186],\
    120 [0, 0, 1, 0, -333],\
    121 [0, 0, 1, 0, 8984],\
    122 [0, 0, 0, 0, -10000],\
    123 [0, 0, 0, 0, 270000],\
    124 [0, 0, 0, 0, -100],\
    125 [0, 0, 0, 0, 2700],\
    126 [0, 0, 0, -5324, 0],\
    127 [0, 0, 0, 1331, 0],\
    128 [0, 0, 0, 0, -81],\
    129 [0, 0, 0, 0, 3],\
    130 [0, 0, 0, 0, -324],\
    131 [0, 0, 0, 0, 12],\
    132 [0, 0, 0, 0, -1296],\
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    134 [0, 0, 0, 0, -1581228],\
    135 [0, 0, 0, 0, 58564],\
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    139 [0, 0, 0, -1815, -29282],\
    140 [0, 0, 0, 0, -1331],\
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    142 [0, 0, 1, -33083930, -73244287055],\
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    146 [0, 0, 1, 0, -2506228],\
    147 [0, 0, 1, 0, 92823],\
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    152 [0, 0, 0, 0, -67228],\
    153 [0, 0, 0, 0, 1815156],\
    154 [0, 0, 0, 0, -5292],\
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    156 [0, 0, 0, 0, -7],\
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    158 [0, 0, 0, -2197, 0],\
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    160 [0, 0, 0, -1859, -30758],\
    161 [0, 0, 0, -1859, 30758],\
    162 [0, 0, 0, -169, 0],\
    163 [0, 0, 0, 676, 0],\
    164 [1, -1, 1, -220485, -39791650],\
    165 [1, -1, 1, -12970, -695824],\
    166 [1, -1, 1, -4500, 117296],\
    167 [1, -1, 1, -265, 2104],\
    168 [0, 0, 1, 0, -7594],\
    169 [0, 0, 1, 0, 281],\
    170 [0, 0, 1, 0, -37969],\
    171 [0, 0, 1, 0, 1406],\
    172 [0, 0, 1, 0, -1519],\
    173 [0, 0, 1, 0, 56],\
    174 [0, 0, 1, 0, -189844],\
    175 [0, 0, 1, 0, 7031],\
    176 [0, 0, 1, 0, -304],\
    177 [0, 0, 1, 0, 11],\
    178 [0, 0, 0, -10, 0],\
    179 [0, 0, 0, 40, 0],\
    180 [0, 0, 0, -50, 0],\
    181 [0, 0, 0, 200, 0],\
    182 [0, 0, 0, -250, 0],\
    183 [0, 0, 0, 1000, 0],\
    184 [0, -1, 0, -333, -1963],\
    185 [0, -1, 0, -83, 287],\
    186 [0, 0, 0, 0, -756],\
    187 [0, 0, 0, 0, 28],\
    188 [0, 0, 0, -6615, -203742],\
    189 [0, 0, 0, -735, 7546],\
    190 [0, 0, 0, 0, -9261],\
    191 [0, 0, 0, 0, 343],\
    192 [0, 0, 0, 0, -7260624],\
    193 [0, 0, 0, 0, 268912],\
    194 [0, 0, 0, -2475, -47250],\
    195 [0, 0, 0, -2475, 47250],\
    196 [0, 0, 0, -225, 0],\
    197 [0, 0, 0, 900, 0],\
    198 [0, 0, 0, -13500, 0],\
    199 [0, 0, 0, 3375, 0],\
    200 [0, 0, 0, -45, 0],\
    201 [0, 0, 0, 180, 0],\
    202 [0, 0, 0, -60, 0],\
    203 [0, 0, 0, 15, 0],\
    204 [0, 0, 0, -2700, 0],\
    205 [0, 0, 0, 675, 0],\
    206 [0, 0, 1, 0, -138450256],\
    207 [0, 0, 1, 0, 5127787],\
    208 [0, 0, 0, -5324, -149072],\
    209 [0, 0, 0, -5324, 149072],\
    210 [0, 0, 0, -484, 0],\
    211 [0, 0, 0, 121, 0],\
    212 [0, 1, 0, -3549, -84691],\
    213 [0, 1, 0, -29, 53],\
    214 [0, 0, 1, 0, -9584035],\
    215 [0, 0, 1, 0, 354964],\
    216 [0, 0, 1, 0, -563767],\
    217 [0, 0, 1, 0, 20880],\
    218 [0, 0, 1, -78030, -8390176],\
    219 [0, 0, 1, -8670, 310747],\
    220 [0, 0, 1, 0, -33163],\
    221 [0, 0, 1, 0, 1228],\
    222 [0, 0, 1, 0, -115],\
    223 [0, 0, 1, 0, 4],\
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    228 [0, 0, 1, 0, -6233767],\
    229 [0, 0, 1, 0, 230880],\
    230 [0, 0, 1, -342950, -77378094],\
    231 [0, 0, 1, -950, 11281],\
    232 [0, 0, 0, -17, 0],\
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    234 [0, 0, 1, 0, -2437],\
    235 [0, 0, 1, 0, 90],\
    236 [0, 0, 0, 0, -459],\
    237 [0, 0, 0, 0, 17],\
    238 [0, 0, 0, 0, -7803],\
    239 [0, 0, 0, 0, 289],\
    240 [0, 0, 0, 0, -2255067],\
    241 [0, 0, 0, 0, 83521],\
    242 [0, 0, 0, 0, -25],\
    243 [0, 0, 0, 0, 675],\
    244 [0, 0, 0, 0, -20],\
    245 [0, 0, 0, 0, 540],\
    246 [0, 0, 0, -108000, 13662000],\
    247 [0, 0, 0, -12000, -506000],\
    248 [0, 0, 0, 0, -2000],\
    249 [0, 0, 0, 0, 54000],\
    250 [0, 0, 0, 0, -2500],\
    251 [0, 0, 0, 0, 67500],\
    252 [0, 0, 0, 0, -3125],\
    253 [0, 0, 0, 0, 84375],\
    254 [0, 0, 0, -52, 0],\
    255 [0, 0, 0, 13, 0],\
    256 [0, 0, 0, -8788, 0],\
    257 [0, 0, 0, 2197, 0],\
    258 [0, 0, 1, 0, -53594],\
    259 [0, 0, 1, 0, 1447031],\
    260 [0, 0, 1, 0, -44],\
    261 [0, 0, 1, 0, 1181],\
    262 [0, 0, 1, 0, -50646094],\
    263 [0, 0, 1, 0, 1875781],\
    264 [0, 0, 1, 0, -41344],\
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    266 [1, -1, 0, -409992, -100936459],\
    267 [1, -1, 0, -24117, -1766584],\
    268 [1, -1, 0, -8367, 296666],\
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   3180 [0, 0, 0, -340, 0],\
   3181 [0, 0, 0, 85, 0],\
   3182 [0, 0, 0, -98260, 0],\
   3183 [0, 0, 0, 24565, 0],\
   3184 [0, 0, 0, -144500, 0],\
   3185 [0, 0, 0, 36125, 0],\
   3186 [0, 0, 0, -8500, 0],\
   3187 [0, 0, 0, 2125, 0],\
   3188 [0, 0, 0, -2456500, 0],\
   3189 [0, 0, 0, 614125, 0],\
   3190 [0, 0, 0, -5780, 0],\
   3191 [0, 0, 0, 1445, 0],\
   3192 [0, 0, 1, -4633470, 3839177405],\
   3193 [0, 0, 1, -514830, -142191756],\
   3194 [0, 0, 1, 0, -562023],\
   3195 [0, 0, 1, 0, 15174614],\
   3196 [0, 0, 0, 0, -39204],\
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   3198 [0, 0, 0, 0, -527076],\
   3199 [0, 0, 0, 0, 14231052],\
   3200 [0, 0, 0, 0, -18974736],\
   3201 [0, 0, 0, 0, 702768],\
   3202 [0, 0, 0, 0, -1089],\
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   3204 [0, 0, 0, 0, -1293732],\
   3205 [0, 0, 0, 0, 47916],\
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   3207 [0, 0, 0, 0, 99],\
   3208 [0, 0, 0, 0, -626166288],\
   3209 [0, 0, 0, 0, 23191344],\
   3210 [0, 0, 0, 0, -42768],\
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   3212 [0, 0, 0, 0, -156541572],\
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   3224 [0, 0, 0, 0, -39135393],\
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   3243 [0, 0, 0, 0, 330625],\
   3244 [0, 0, 0, 0, -71875],\
   3245 [0, 0, 0, 0, 1940625],\
   3246 [0, 0, 0, -1785375, 903399750],\
   3247 [0, 0, 0, -198375, -33459250],\
   3248 [0, 0, 0, 0, -1520875],\
   3249 [0, 0, 0, 0, 41063625],\
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   3251 [0, 0, 0, 0, 868906305],\
   3252 [0, 0, 0, 0, -3218171500],\
   3253 [0, 0, 0, 0, 86890630500],\
   3254 [0, 0, 0, 0, -460],\
   3255 [0, 0, 0, 0, 12420],\
   3256 [0, 0, 0, 0, -152087500],\
   3257 [0, 0, 0, 0, 4106362500],\
   3258 [0, 0, 0, 0, -7141500],\
   3259 [0, 0, 0, 0, 264500],\
   3260 [0, 0, 0, 0, -151114140],\
   3261 [0, 0, 0, 0, 5596820],\
   3262 [0, 0, 0, 0, -23611584375],\
   3263 [0, 0, 0, 0, 874503125],\
   3264 [0, 0, 0, 0, -71415],\
   3265 [0, 0, 0, 0, 2645],\
   3266 [0, 0, 1, 0, -2112079867],\
   3267 [0, 0, 1, 0, 78225180],\
   3268 [0, 0, 1, 0, -898],\
   3269 [0, 0, 1, 0, 33],\
   3270 [0, 0, 1, 0, -1486278425],\
   3271 [0, 0, 1, 0, 40129517468],\
   3272 [0, 0, 1, 0, -632],\
   3273 [0, 0, 1, 0, 17057],\
   3274 [0, 0, 1, 0, -4117115],\
   3275 [0, 0, 1, 0, 111162098],\
   3276 [0, 0, 1, 0, -324088],\
   3277 [0, 0, 1, 0, 12003],\
   3278 [0, 0, 1, 0, -116995678],\
   3279 [0, 0, 1, 0, 4333173],\
   3280 [0, 0, 1, 0, -5850637],\
   3281 [0, 0, 1, 0, 216690],\
   3282 [0, 0, 1, 0, -228062],\
   3283 [0, 0, 1, 0, 6157667],\
   3284 [0, 0, 1, 0, -11405],\
   3285 [0, 0, 1, 0, 307928],\
   3286 [0, 0, 0, -20172, 0],\
   3287 [0, 0, 0, 5043, 0],\
   3288 [0, 0, 0, -369, 0],\
   3289 [0, 0, 0, 1476, 0],\
   3290 [0, 0, 0, -620289, 0],\
   3291 [0, 0, 0, 2481156, 0],\
   3292 [0, 0, 0, -7443468, 0],\
   3293 [0, 0, 0, 1860867, 0],\
   3294 [0, 0, 0, -4428, 0],\
   3295 [0, 0, 0, 1107, 0],\
   3296 [0, 0, 0, -87, 0],\
   3297 [0, 0, 0, 348, 0],\
   3298 [0, 0, 0, -73167, 0],\
   3299 [0, 0, 0, 292668, 0],\
   3300 [0, 0, 0, -333036, -73752336],\
   3301 [0, 0, 0, -333036, 73752336],\
   3302 [0, 0, 0, -30276, 0],\
   3303 [0, 0, 0, 7569, 0],\
   3304 [0, 0, 0, 0, -22632992],\
   3305 [0, 0, 0, 0, 611090784],\
   3306 [0, 0, 0, -454140, -115896528],\
   3307 [0, 0, 0, -50460, 4292464],\
   3308 [0, 0, 0, 0, -5268024],\
   3309 [0, 0, 0, 0, 195112],\
   3310 [0, 0, 0, 0, -1107602046],\
   3311 [0, 0, 0, 0, 41022298],\
   3312 [0, 0, 0, 0, -45414],\
   3313 [0, 0, 0, 0, 1682],\
   3314 [0, 0, 0, 0, -1682],\
   3315 [0, 0, 0, 0, 45414],\
   3316 [0, 0, 0, 0, -25056],\
   3317 [0, 0, 0, 0, 928],\
   3318 [0, 0, 0, -658503, 0],\
   3319 [0, 0, 0, 2634012, 0],\
   3320 [0, 0, 0, -783, 0],\
   3321 [0, 0, 0, 3132, 0],\
   3322 [0, 0, 0, 0, -67],\
   3323 [0, 0, 0, 0, 1809],\
   3324 [0, 0, 0, 0, -121203],\
   3325 [0, 0, 0, 0, 4489],\
   3326 [0, 0, 0, 0, -2176321068],\
   3327 [0, 0, 0, 0, 80604484],\
   3328 [0, 0, 0, 0, -268],\
   3329 [0, 0, 0, 0, 7236],\
   3330 [0, 0, 0, 0, -1350125107],\
   3331 [0, 0, 0, 0, 36453377889],\
   3332 [0, 0, 1, -18779942, -31355460662],\
   3333 [0, 0, 1, -52022, 4571433],\
   3334 [0, 0, 1, 0, -294],\
   3335 [0, 0, 1, 0, 7931],\
   3336 [0, 0, 1, 0, -823446169],\
   3337 [0, 0, 1, 0, 30498006],\
   3338 [0, 0, 1, 0, -1863844],\
   3339 [0, 0, 1, 0, 69031],\
   3340 [0, 0, 1, 0, -16222344],\
   3341 [0, 0, 1, 0, 438003281],\
   3342 [0, 0, 0, 0, -4244832],\
   3343 [0, 0, 0, 0, 157216],\
   3344 [0, 0, 0, 0, -45435424],\
   3345 [0, 0, 0, 0, 1226756448],\
   3346 [0, 0, 0, 0, -249696],\
   3347 [0, 0, 0, 0, 9248],\
   3348 [0, 0, 0, 0, -72162144],\
   3349 [0, 0, 0, 0, 2672672],\
   3350 [0, 0, 0, 0, -544],\
   3351 [0, 0, 0, 0, 14688],\
   3352 [0, 0, 0, 0, -14688],\
   3353 [0, 0, 0, 0, 544],\
   3354 [0, 0, 0, 0, -2672672],\
   3355 [0, 0, 0, 0, 72162144],\
   3356 [0, 0, 0, 0, -9248],\
   3357 [0, 0, 0, 0, 249696],\
   3358 [0, 0, 0, 0, -1226756448],\
   3359 [0, 0, 0, 0, 45435424],\
   3360 [0, 0, 0, 0, -157216],\
   3361 [0, 0, 0, 0, 4244832]]
	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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