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…or describe it by its bases, non-bases or lines
Matroid

Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id. Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as 123 145. Lines are the lines with at least three points of a simple rank-3 matroid. A revlex encoding is a string of * and 0.

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Invariants
Realizability
Properties

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5,849,183 matroids, showing 22,201–22,250

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.1845813111481✓all1rational
3.11.1845823111481✓all1rational
3.11.1845843111481✓all1rational
3.11.1845883111492✓all but 21rational
3.11.1845923111481✓all1genus 1 curve (11a3)
3.11.1845953111481✓all1rational
3.11.1845983111481✓all1rational
3.11.1846003111464✓all1rational
3.11.1846013111484✓all1empty
3.11.1846023111482✓all1empty
3.11.1846083111492✓all1rational
3.11.1846093111514✓all1rational
3.11.1846113111501✓all1rational
3.11.1846133111501✓all1rational
3.11.1846143111491✓all but 2,31rational
3.11.1846163111492✓all1rational
3.11.1846173111491✓all but 21rational
3.11.1846193111481✓all1rational
3.11.1846203111491✓all1rational
3.11.1846213111481✓all1rational
3.11.1846233111482✓all but 21rational
3.11.1846303111492✓all1rational
3.11.1846313111491✓all1rational
3.11.1846333111482✓all1rational over Q(a)/(a^2 - a - 1)
3.11.1846363111472✓all1point over Q(a)/(a^2 - a - 1)
3.11.1846393111494✓all1empty
3.11.1846403111482✓all1empty
3.11.1846413111484✓all but 21empty
3.11.1846443111492✓all1rational
3.11.1846453111492✓all1rational
3.11.1846473111492✓all1rational
3.11.1846533111501✓all but 21rational
3.11.1846543111491✓all but 2,51rational
3.11.1846563111492✓all but 21rational
3.11.1846583111502✓all1rational
3.11.1846593111492✓all but 2,3,51rational
3.11.1846613111491✓all but 21rational
3.11.1847023111492✓all but 21rational
3.11.1847073111481✓all1rational
3.11.1847363111481✓all1rational
3.11.1847383111481✓all1rational
3.11.1847403111481✓all but 21rational
3.11.1847413111481✓all1rational
3.11.1847453111488✓all1rational
3.11.1847463111532✓all1rational
3.11.1847483111522✓all1rational
3.11.1847543111522✓all but 21rational
3.11.1847553111522✓all1rational
3.11.1847563111521✓all1rational
3.11.1847593111511✓all1rational

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