The database currently contains 725,187 elliptic curves in 350,509 isogeny classes, over 423 number fields of degree 2 to 6. Elliptic curves defined over $\mathbb{Q}$ are contained in a separate database. Here are some further statistics.

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 By real quadratic field: $$\Q(\sqrt{2})$$   $$\Q(\sqrt{3})$$   $$\Q(\sqrt{5})$$   $$\Q(\sqrt{6})$$   $$\Q(\sqrt{7})$$   $$\Q(\sqrt{10})$$   $$\Q(\sqrt{11})$$   $$\Q(\sqrt{13})$$   $$\Q(\sqrt{14})$$   $$\Q(\sqrt{15})$$   $\cdots$ By imaginary quadratic field: $$\Q(\sqrt{-1})$$   $$\Q(\sqrt{-2})$$   $$\Q(\sqrt{-3})$$   $$\Q(\sqrt{-5})$$   $$\Q(\sqrt{-6})$$   $$\Q(\sqrt{-7})$$   $$\Q(\sqrt{-10})$$   $$\Q(\sqrt{-11})$$   $$\Q(\sqrt{-13})$$   $\cdots$ By cubic field: 3.1.23.1   $$\Q(\zeta_{7})^+$$   $$\Q(\zeta_{9})^+$$   3.3.148.1   3.3.169.1   3.3.229.1   3.3.257.1   3.3.316.1   $\cdots$ By totally real quartic field: 4.4.725.1   $$\Q(\zeta_{15})^+$$   $$\Q(\sqrt{2}, \sqrt{5})$$   4.4.1957.1   $$\Q(\zeta_{20})^+$$   $$\Q(\zeta_{16})^+$$   4.4.2225.1   $$\Q(\sqrt{2}, \sqrt{3})$$   $\cdots$ By totally real quintic field: $$\Q(\zeta_{11})^+$$   5.5.24217.1   5.5.36497.1   5.5.38569.1   5.5.65657.1   5.5.70601.1   5.5.81509.1   $\cdots$ By totally real sextic field: 6.6.300125.1   $$\Q(\zeta_{13})^+$$   6.6.434581.1   $$\Q(\zeta_{21})^+$$   6.6.485125.1   6.6.592661.1   6.6.703493.1   $\cdots$ Some interesting elliptic curves or a random elliptic curve

## Find

 Label e.g. 2.2.5.1-31.1-a1 or 2.2.5.1-31.1-a

*The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.