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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 21,151–21,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71405 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71406 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71409 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71411 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71413 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71420 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71426 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71433 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71457 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71458 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71459 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71460 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71463 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71464 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71466 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71467 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71474 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71479 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71486 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71552 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71553 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71554 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71556 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71557 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71558 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71560 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71561 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71562 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71563 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71565 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71566 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71567 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71575 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.71576 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71577 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71579 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71580 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71581 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71583 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71584 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71585 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71593 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71594 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71595 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71597 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71598 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71599 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71601 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71602 | 3 | 11 | 151 | 1 | ✓ | all | 3 | genus 1 curve (37a1) x P^1 |
| 3.11.71603 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |