The **isogeny class (over a field $K$)** of an elliptic curve $E$ defined over $K$ is the set of all isomorphism classes of elliptic curves defined over $K$ that are isogenous to $E$ over $K$. Over a number field $K$ this is always a finite set.

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-06-18 21:24:04

**Referred to by:**

- ec.curve_label
- ec.isogeny
- ec.isogeny_graph
- ec.isogeny_matrix
- ec.q.cremona_label
- ec.q.lmfdb_label
- ec.rank
- rcs.cande.lfunction
- lmfdb/ecnf/ecnf_stats.py (lines 30-31)
- lmfdb/ecnf/templates/ecnf-curve.html (lines 389-396)
- lmfdb/ecnf/templates/ecnf-search-results.html (line 136)
- lmfdb/elliptic_curves/templates/ec-index.html (line 63)
- lmfdb/elliptic_curves/templates/ec-index.html (line 151)
- lmfdb/elliptic_curves/templates/ec-search-results.html (line 55)
- lmfdb/elliptic_curves/templates/ec-search-results.html (line 133)

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