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elliptic curve

a smooth projective curve of genus 1 equipped with a rational basepoint
Class type of: hyperelliptic curve, abelian variety, cubic plane curve Q268493

Facts

5 properties
Subclass of
hyperelliptic curve, abelian variety, cubic plane curve
Has use
elliptic curve cryptography[4]
Different from
ellipse[5]
Maintained by WikiProject
WikiProject Mathematics[7]
Studied by
elliptic curve theory[6]
🏷️ Also known as
en elliptic curve ar منحنى إهليلجي cs eliptické křivky cs eliptická křivka da elliptisk kurve de elliptische Kurven de Elliptische Kurven de Weierstrassgleichung de elliptische Kurve de Weierstraßgleichung de Weierstraß-Gleichung de Weierstrass-Gleichung el ελλειπτική καμπύλη es curva eliptica es curva elíptica es curvas elipticas es curvas elípticas fa منحنی بیضوی fi elliptinen käyrä fi elliptinen yhtälö
🔖 Identifiers · 29
Library of Congress authority ID
sh85034918
GND ID
4014487-2
OpenAlex ID
C179603306
BNCF Thesaurus ID
35523
BabelNet ID
00141700n
Bibliothèque nationale de France ID
11990345h
Brilliant Wiki ID
elliptic-curves
Dewey Decimal Classification
516.352
Encyclopedia of Mathematics article ID
Elliptic_curve
Encyclopædia Britannica Online ID
topic/elliptic-curve, topic/elliptic-equation
Freebase ID
/m/02s3f
GitLab topic ID
elliptic+curves
Show all 29 identifiers +17
Great Russian Encyclopedia Online ID (2017)
4931039
Great Russian Encyclopedia portal ID
ellipticheskaia-krivaia-43db53
Group Properties article ID
Elliptic_curve_group
KBpedia ID
EllipticalCurve
Lex ID
elliptisk_kurve
MathWorld ID
EllipticCurve
Mathematics Subject Classification ID
11G05
Microsoft Academic ID (discontinued)
179603306
NL CR AUT ID
ph520058
National Library of Israel J9U ID
987007538488105171
Online PWN Encyclopedia ID
3897559
ProofWiki ID
Definition:Elliptic_Curve
Stack Exchange tag
stackoverflow.com
Topic's main category
Category:Elliptic curves
Treccani's Enciclopedia della Matematica ID
curva-ellittica
Yale LUX ID
concept/7af7b6f9-4c82-406a-8b69-974f1ac30b6b
Zhihu topic ID
19671036

Report an error or request removal Lineage (PROV-JSON)

🔗 Connections
← Field of work 7
Alfred George Greenhill, Heinrich Schröter, Karl Rubin, J. W. S. Cassels, Fred Irvin Diamond, Henri Darmon, Vladimír Sedláček
Subclass of 3
abelian variety, cubic plane curve, hyperelliptic curve
Subtypes 3
Edwards curve, Montgomery curve, Mordell curve
Named after 2
Elliptic-curve Diffie–Hellman, hyperelliptic curve
Different from 1
ellipse
Has use 1
elliptic curve cryptography
Maintained by WikiProject 1
WikiProject Mathematics
Topic's main category 1
Category:Elliptic curves
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Summary

elliptic curve is a type of hyperelliptic curve[1], abelian variety[2], and cubic plane curve[3].

Body

Influence

Things named for elliptic curve include Elliptic-curve Diffie–Hellman[8], a key-agreement protocol[9] and hyperelliptic curve[10].

Why It Matters

Entities named for elliptic curve include Elliptic-curve Diffie–Hellman[8], a key-agreement protocol[9] and hyperelliptic curve[10].

Related Entities

Vladimír Sedláček

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [1] ↑ . wikidata.org.
  2. [2] ↑ . wikidata.org.
  3. [3] ↑ . wikidata.org.
  4. [4] ↑ . wikidata.org.
  5. [5] ↑ . wikidata.org.
  6. [6] ↑ . wikidata.org.
  7. [7] ↑ . wikidata.org.

Inverse relationships (entities pointing at this one)

  1. [8] ↑ . wikidata.org. → on this site
  2. [10] ↑ . wikidata.org. → on this site

Inline context (facts about related entities)

  1. [9] ↑ . Wikidata. wikidata.org. → on this site

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). elliptic curve. Retrieved November 5, 2026, from https://4ort.xyz/entity/elliptic-curve
MLA “elliptic curve.” 4ort.xyz Knowledge Graph, 4ort.xyz, 5 Nov. 2026, https://4ort.xyz/entity/elliptic-curve.
BibTeX @misc{4ortxyz_elliptic-curve_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{elliptic curve}}, year = {2026}, url = {https://4ort.xyz/entity/elliptic-curve}, note = {Accessed: 2026-11-05}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): elliptic curve — https://4ort.xyz/entity/elliptic-curve (retrieved 2026-11-05)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 19w ago · Charp238 · 2026-06-24 view diff on Wikidata ↗
    Schematic → ECClines.svg
    "/* wbsetclaim-create:2||1 */ Schematic: ECClines.svg"
  2. 23w ago · Twofivesixbot bot · 2026-05-25 view diff on Wikidata ↗
    Has use → elliptic curve cryptography
    Studied by → elliptic curve theory
    Subclass of → hyperelliptic curve, abelian variety, cubic plane curve
    Maintained by WikiProject → WikiProject Mathematics
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|2 */ National Library of Israel J9U ID: 987007538488105171, mv to monolingual text names on J9U statements"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.