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The database currently contains the Cremona database of all 2,483,649 elliptic curves in 1,741,002 isogeny classes, with conductor at most 400,000, all of which have rank ≤ 4.

Distribution of rank

Rank 0 1 2 3 4
number of curves 956086 1246537 274346 6679 1
number of isogeny classes 639862 875337 219508 6294 1
proportion 36.75% 50.28% 12.61% 0.36% 0.00%

Distribution of torsion

Torsion structure \(C_{1}\) \(C_{2}\) \(C_{3}\) \(C_{4}\) \(C_{5}\) \(C_{6}\) \(C_{7}\) \(C_{8}\) \(C_{9}\) \(C_{10}\) \(C_{12}\)
Torsion order 1 2 3 4 5 6 7 8 9 10 12
number of curves 1349242 969444 43586 28645 1309 5945 76 162 18 42 16
proportion 54.32% 39.03% 1.75% 1.15% 0.05% 0.24% 0.00% 0.01% 0.00% 0.00% 0.00%
 
Torsion structure   \(C_{2}\times C_{2}\)   \(C_{2}\times C_{4}\)   \(C_{2}\times C_{6}\) \(C_{2}\times C_{8}\)
Torsion order   4   8   12 16
number of curves   83542   1523   93 6
proportion   3.36%   0.06%   0.00% 0.00%

Distribution of Ш\(_{an} \)

Ш\(_{an} \) \(1^2\) \(2^2\) \(3^2\) \(4^2\) \(5^2\) \(6^2\) \(7^2\) \(8^2\) \(9^2\) \(10^2\) \(11^2\) \(12^2\)
number of curves 2291488 125537 39939 14136 6737 1818 1676 999 436 236 232 96
 
Ш\(_{an} \) \(13^2\) \(14^2\) \(15^2\) \(16^2\) \(17^2\) \(18^2\) \(19^2\) \(20^2\) \(21^2\) \(22^2\) \(23^2\) \(24^2\)
number of curves 112 40 29 34 23 3 19 13 3 2 11 4
   
Ш\(_{an} \) \(25^2\) \(26^2\) \(27^2\) \(28^2\) \(29^2\) \(31^2\) \(33^2\) \(41^2\) \(47^2\) \(50^2\) \(75^2\)
number of curves 9 3 1 4 2 2 1 1 1 1 1