Elliptic curves over $\Q$

The database currently includes 3,824,372 elliptic curves defined over $\Q$, in 2,917,287 isogeny classes, with conductor at most 299,996,953. Here are some further statistics and completeness information.

Browse

By conductor:	1-99   100-999   1000-9999   10000-99999   100000-500000   >500000
By rank:	0  1  2  3  4  5
By torsion order:	1  2  3  4  5  6  7  8  9  10  12  16
Some interesting elliptic curves or a random elliptic curve

Search

Conductor		e.g. 389 or 100-200	Bad primes $p$		e.g. 5,13
Discriminant		e.g. 389 or 100-200	j-invariant		e.g. 1728 or -4096/11
Torsion		e.g. C3	Complex multiplication		e.g. potential CM by Q(i)
Rank		e.g. 0	Analytic order of Ш		e.g. 4
Regulator		e.g. 8.4-9.1	$p$ dividing |Ш|		e.g. 3,5
Galois image		e.g. 13S4 or 13.91.3.2	Nonmaximal $\ell$		e.g. 2,3
Isogeny class size		e.g. 4	Isogeny class degree		e.g. 16
Integral points		e.g. 2 or 4-15	Cyclic isogeny degree		e.g. 16
Curves per isogeny class		e.g. all, one	Reduction		e.g. semistable
Results to display			Faltings height		e.g. -1-2

Display:

Find

Label or coefficients
	e.g. 11.a2 or 389.a or 11a1 or 389a or [0,1,1,-2,0] or [-3024, 46224] or y^2 = x^3 + 1