Elliptic Curves over $\Q$

The database currently contains the complete Cremona database. This contains all 3,064,705 elliptic curves defined over $\Q$ with conductor at most 500,000. Here are some further statistics.

Browse elliptic curves over $\Q$

By conductor: 1-99 100-999 1000-9999 10000-99999 100000-500000

By rank: 0 1 2 3 4

By torsion order: 1 2 3 4 5 6 7 8 9 10 12 16

A random elliptic curve from the database

Find a specific curve or isogeny class by coefficients, LMFDB label, or Cremona label

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Conductor		e.g. 389 or 100-200	j-invariant		e.g. 1728 or -4096/11
Rank		e.g. 0	CM
Torsion order		e.g. 2	Torsion structure
Analytic order of Ш		e.g. 4	Curves per isogeny class
Maximal primes		e.g. 2,3	Non-maximal primes		e.g. 2,3
Cyclic isogeny degree		e.g. 16	Bad primes		e.g. 5,13
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