︠7e14dcee-0dd8-4c68-88aa-d523ef65abf3i︠ %md Number of times there are this many curves of prime conductor $p < 2\cdot 10^{13}$, in the range of Benett's data. 1 4617822856 2 54999476 3 6647765 4 386047 5 91229 6 20116 7 5306 8 1697 9 726 10 321 11 116 12 50 13 24 14 12 15 5 16 8 17 3 18 2 19 1 20 1 21 1 ︡54bdbb50-d577-407c-84cd-cea9a2f8af1c︡{"done":true,"md":"\nNumber of times there are this many curves of prime conductor $p < 2\\cdot 10^{13}$, in the range of Benett's data.\n\n 1 4617822856\n 2 54999476\n 3 6647765\n 4 386047\n 5 91229\n 6 20116\n 7 5306\n 8 1697\n 9 726\n 10 321\n 11 116\n 12 50\n 13 24\n 14 12\n 15 5\n 16 8\n 17 3\n 18 2\n 19 1\n 20 1\n 21 1"} ︠6fa3dadf-0647-4a40-9de8-87ce374eac19s︠ v = [[1 , 4617822856], [2 , 54999476], [3 , 6647765], [4 , 386047], [5 , 91229], [6 , 20116], [7 , 5306], [8 , 1697], [9 , 726], [10, 321], [11, 116], [12, 50], [13, 24], [14, 12], [15, 5], [16, 8], [17, 3], [18, 2], [19, 1], [20, 1], [21, 1]] ︡71ad21ad-97f4-4974-9e79-66eec5c821de︡{"done":true}︡ ︠e01fb4be-81fd-434e-b2c9-f3e239b478e7s︠ line2d([[a[0], log(a[1])] for a in v], marker='.', markersize=20, aspect_ratio=1/5, frame=True, ymin=-2, xmin=-1, gridlines=True, figsize=13) ︡196819ae-b432-471d-a66a-1d10eaccee94︡{"file":{"filename":"/projects/95d92fa7-cb50-414e-a35d-9897eabe44de/.sage/temp/compute4-us/2574/tmp_ESm4ie.svg","show":true,"text":null,"uuid":"ecf44c43-057f-40b8-9966-06b177b94174"},"once":false}︡{"html":"
"}︡{"done":true}︡ ︠633a9a1d-f86f-4f19-bf92-457498ebaad8s︠ -10/4. ︡f9756494-990a-4100-886d-5a3384d8d52e︡{"stdout":"-2.50000000000000\n"}︡{"done":true}︡ ︠4ed36074-9756-4f5e-a781-bb19c360b629s︠ db = CremonaDatabase() ︡735e78aa-cd02-4df9-9591-0248deb61b8c︡{"done":true}︡ ︠13b4dc6e-76e3-43f1-981e-91a466923c40s︠ db.number_of_isogeny_classes(37) ︡f76a483c-60f9-4e98-a781-bfda52089630︡{"stdout":"2\n"}︡{"done":true}︡ ︠abf45cb3-ac26-42ea-b096-c588f1a4ea47s︠ %time cnts = [db.number_of_isogeny_classes(p) for p in primes(300000)] ︡3a5957f5-6a67-4458-9015-873051a3622c︡{"stdout":"CPU time: 1.26 s, Wall time: 2.85 s"}︡{"stdout":"\n"}︡{"done":true}︡ ︠83c8d2ed-7929-4d14-88c1-4784f332fc70s︠ set(cnts) ︡0d79ddd4-cac4-410d-9ea8-5454bcd45f88︡{"stdout":"set([0, 1, 2, 3, 4, 5, 7])\n"}︡{"done":true}︡ ︠aa7921a3-1496-4aff-aa4f-7aa1a8034f40s︠ w = [[i,cnts.count(i)] for i in [1..7]] w ︡5fd80617-1100-44ea-8675-848330d19eee︡{"stdout":"[[1, 2745], [2, 275], [3, 98], [4, 24], [5, 5], [6, 0], [7, 1]]\n"}︡{"done":true}︡ ︠9892da4a-05dd-4151-88d1-fdb2559e60ebs︠ line2d([[a[0], max(-1,log(a[1]))] for a in w], marker='.', markersize=20, frame=True, gridlines=True) ︡c50f2aa3-7b16-4fe6-b5bd-c7291366d215︡{"file":{"filename":"/projects/95d92fa7-cb50-414e-a35d-9897eabe44de/.sage/temp/compute4-us/2574/tmp_YXrHVY.svg","show":true,"text":null,"uuid":"bc22479d-6bfe-45a7-970b-1d6741abe29c"},"once":false}︡{"html":"
"}︡{"done":true}︡ ︠3bab45ee-75ca-4f1a-bfb3-51f1bfb32c5dss︠ -6/4. ︡cf9de3e3-1a4c-4a50-9c22-7277b2a3b5d7︡{"stdout":"-1.50000000000000\n"}︡{"done":true}︡ ︠fa70cb81-3670-4618-8c99-a311bee39d7c︠