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Currently, the database includes 3,824,372 elliptic curves in 2,917,287 isogeny classes, with conductor at most 299,996,953.

Distribution of rank

rank 0 1 2 3 4 5 7 28 2021 \(\mathrm{avg}\ 0.78\)
count 1404510 1887132 493291 37334 2086 19 0 0 0 3824372
proportion 36.73% 49.34% 12.90% 0.98% 0.05% 0.00% 0.00% 0.00% 0.00% 100.00%

Distribution of torsion subgroups

torsion structure trivial $C_{2}$ $C_{2} \times C_{2}$ $C_{2} \times C_{4}$ $C_{2} \times C_{6}$ $C_{2} \times C_{8}$ $C_{3}$ $C_{4}$ $C_{5}$ $C_{6}$
count 2436622 1192275 100058 1737 96 6 51421 33558 1503 6759
proportion 63.71% 31.18% 2.62% 0.05% 0.00% 0.00% 1.34% 0.88% 0.04% 0.18%
torsion structure $C_{7}$ $C_{8}$ $C_{9}$ $C_{10}$ $C_{12}$
count 80 178 20 42 17
proportion 0.00% 0.00% 0.00% 0.00% 0.00%

Distribution of analytic order of Ш

sha $1^2$ $2^2$ $3^2$ $4^2$ $5^2$ $6^2$ $7^2$ $8^2$ $9^2$ $10^2$
count 3502608 212138 65936 22749 10953 3239 2795 1512 853 391
proportion 91.59% 5.55% 1.72% 0.59% 0.29% 0.08% 0.07% 0.04% 0.02% 0.01%
sha $11^2$ $12^2$ $13^2$ $14^2$ $15^2$ $16^2$ $17^2$ $18^2$ $19^2$ $20^2$
count 408 174 210 70 89 49 50 15 36 17
proportion 0.01% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
sha $21^2$ $22^2$ $23^2$ $24^2$ $25^2$ $26^2$ $27^2$ $28^2$ $29^2$ $31^2$
count 10 3 15 4 13 3 5 7 3 4
proportion 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
sha $32^2$ $33^2$ $34^2$ $37^2$ $41^2$ $43^2$ $47^2$ $50^2$ $75^2$ Total
count 5 1 1 1 1 1 1 1 1 3824372
proportion 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00%