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The database currently contains 725,223 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

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Base field e.g. 2.2.5.1 or Qsqrt5 Base field degree/signature
Conductor norm e.g. 31 or 1-100 Bad primes e.g. 5,13
Rank* e.g. 2 $\Q$-curves e.g. base change
Torsion order e.g. 2 Torsion structure
CM discriminant e.g. -4 or -3,-8 CM
Analytic order of Ш* e.g. 4 Regulator* e.g. 8.4-9.1
Cyclic isogeny degree e.g. 16 Curves per isogeny class e.g. all, one
Isogeny class size e.g. 4 Isogeny class degree e.g. 16
Galois image e.g. 7Cs.2.1 or 17B Nonmaximal $\ell$ e.g. 2,3
j-invariant
Results to display Reduction e.g. semistable
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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.