Elliptic curves over number fields

The database currently contains 767,505 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.