The database currently contains the Cremona database of all 3,064,705 elliptic curves in 2,164,260 isogeny classes, with conductor at most 500,000, all of which have rank ≤ 4.

## Distribution of rank

 Rank number of curves number of isogeny classes proportion 0 1 2 3 4 1170876 1535669 348672 9487 1 790258 1086046 279056 8899 1 36.51% 50.18% 12.89% 0.41% 0.00%

## Distribution of torsion

 Torsion structure Torsion order number of curves proportion Torsion structure Torsion order number of curves proportion $$C_{1}$$ $$C_{2}$$ $$C_{3}$$ $$C_{4}$$ $$C_{5}$$ $$C_{6}$$ $$C_{7}$$ $$C_{8}$$ $$C_{9}$$ $$C_{10}$$ $$C_{12}$$ 1 2 3 4 5 6 7 8 9 10 12 1683021 1186350 51405 28645 1503 6759 80 162 20 42 16 54.92% 38.71% 1.68% 0.93% 0.05% 0.22% 0.00% 0.01% 0.00% 0.00% 0.00% $$C_{2}\times C_{2}$$ $$C_{2}\times C_{4}$$ $$C_{2}\times C_{6}$$ $$C_{2}\times C_{8}$$ 4 8 12 16 104846 1753 97 6 3.42% 0.06% 0.00% 0.00%

## Distribution of Ш$$_{an}$$

 Ш$$_{an}$$ number of curves Ш$$_{an}$$ number of curves Ш$$_{an}$$ number of curves $$1^2$$ $$2^2$$ $$3^2$$ $$4^2$$ $$5^2$$ $$6^2$$ $$7^2$$ $$8^2$$ $$9^2$$ $$10^2$$ $$11^2$$ $$12^2$$ 2821178 158758 50428 18170 8501 2402 2153 1301 595 315 300 145 $$13^2$$ $$14^2$$ $$15^2$$ $$16^2$$ $$17^2$$ $$18^2$$ $$19^2$$ $$20^2$$ $$21^2$$ $$22^2$$ $$23^2$$ $$24^2$$ 160 58 43 45 34 7 29 15 5 2 13 4 $$25^2$$ $$26^2$$ $$27^2$$ $$28^2$$ $$29^2$$ $$31^2$$ $$32^2$$ $$33^2$$ $$34^2$$ $$37^2$$ $$41^2$$ $$43^2$$ $$47^2$$ $$50^2$$ $$75^2$$ 12 3 4 7 3 3 4 1 1 1 1 1 1 1 1