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; over $\Q$, it has at most 8 elements by a theorem of Kenku [MR:0675184, 10.1016/0022-314X(82)90025-7].

**Knowl status:**

- Review status: reviewed
- Last edited by Kiran S. Kedlaya on 2019-10-10 14:40:15

**Referred to by:**

- ec.curve_label
- ec.isogeny
- ec.isogeny_graph
- ec.isogeny_matrix
- ec.q.37.a1.bottom
- ec.q.cremona_label
- ec.q.lmfdb_label
- ec.q.optimal
- ec.q.search_input
- ec.rank
- ec.search_input
- rcs.cande.lfunction
- lmfdb/ecnf/ecnf_stats.py (lines 85-86)
- lmfdb/ecnf/main.py (line 730)
- lmfdb/ecnf/templates/ecnf-curve.html (lines 483-491)
- lmfdb/ecnf/templates/ecnf-search-results.html (line 42)
- lmfdb/elliptic_curves/elliptic_curve.py (line 781)
- lmfdb/elliptic_curves/templates/ec-search-results.html (line 23)

**History:**(expand/hide all)

- 2019-10-10 14:40:15 by Kiran S. Kedlaya (Reviewed)
- 2018-06-18 21:24:04 by John Jones (Reviewed)

**Differences**(show/hide)