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…or describe it by its bases, non-bases or lines
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.
6,662,718 matroids, showing 21,101–21,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71258 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.71259 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.71261 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71262 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71264 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71265 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71266 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71267 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71268 | 3 | 11 | 150 | 1 | ✓ | all | 3 | genus 1 curve (11a3) |
| 3.11.71269 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71273 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71275 | 3 | 11 | 150 | 1 | ✓ | all | 3 | empty |
| 3.11.71278 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71279 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.71280 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71281 | 3 | 11 | 150 | 1 | ✓ | all | 3 | empty |
| 3.11.71282 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71285 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71287 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71289 | 3 | 11 | 150 | 2 | ✓ | all | 3 | empty |
| 3.11.71292 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71293 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71294 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71295 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71296 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71299 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71302 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71306 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71307 | 3 | 11 | 150 | 2 | ✓ | all | 3 | genus 1 curve (14a4) |
| 3.11.71308 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71309 | 3 | 11 | 150 | 1 | ✓ | all | 3 | genus 1 curve (11a3) |
| 3.11.71310 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71311 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71315 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71320 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71324 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71328 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71342 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71348 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71349 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71350 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71351 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71355 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71358 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71361 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71367 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71373 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71378 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71403 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71404 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |