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238 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.8.183 | 4 | 8 | 60 | 32 | ✓ | ∅ | -1 | rational |
| 4.8.248 | 4 | 8 | 58 | 192 | ✓ | all | 3 | rational |
| 4.8.259 | 4 | 8 | 59 | 24 | ✓ | all | 1 | empty |
| 4.8.385 | 4 | 8 | 54 | 144 | ✓ | all | 4 | rational |
| 4.8.428 | 4 | 8 | 56 | 6 | ✓ | all | 4 | point over Q(a)/(a^2 - a + 1) |
| 4.8.432 | 4 | 8 | 56 | 4 | ✓ | all | 4 | rational |
| 4.8.442 | 4 | 8 | 52 | 4 | ✓ | all | 2 | rational |
| 4.8.465 | 4 | 8 | 54 | 4 | ✓ | all | 2 | rational |
| 4.8.467 | 4 | 8 | 51 | 12 | ✓ | all | 1 | rational |
| 4.8.483 | 4 | 8 | 51 | 12 | ✓ | all | 2 | rational |
| 4.8.489 | 4 | 8 | 54 | 4 | ✓ | all | 4 | rational |
| 4.8.493 | 4 | 8 | 48 | 24 | ✓ | all | 3 | rational |
| 4.8.501 | 4 | 8 | 53 | 2 | ✓ | all | 4 | rational |
| 4.8.504 | 4 | 8 | 52 | 4 | ✓ | all | 2 | rational |
| 4.8.507 | 4 | 8 | 51 | 4 | ✓ | all | 1 | rational |
| 4.8.510 | 4 | 8 | 51 | 4 | ✓ | {2} | -1 | rational |
| 4.8.512 | 4 | 8 | 49 | 1 | ✓ | all | 5 | rational |
| 4.8.513 | 4 | 8 | 46 | 8 | ✓ | all | 4 | rational |
| 4.8.514 | 4 | 8 | 45 | 8 | ✓ | all | 4 | rational |
| 4.8.517 | 4 | 8 | 50 | 12 | ✓ | all | 3 | rational |
| 4.8.519 | 4 | 8 | 49 | 6 | ✓ | all | 3 | rational |
| 4.8.530 | 4 | 8 | 48 | 24 | ✗ | all | 2 | rational |
| 4.8.545 | 4 | 8 | 47 | 4 | ✗ | all | 1 | rational |
| 4.8.548 | 4 | 8 | 45 | 16 | ✗ | all but 2 | 0 | rational |
| 4.8.549 | 4 | 8 | 46 | 12 | ✗ | all | 3 | rational |
| 4.8.554 | 4 | 8 | 45 | 144 | ✗ | all | 1 | rational |
| 4.8.556 | 4 | 8 | 45 | 24 | ✗ | all | 1 | rational |
| 4.8.561 | 4 | 8 | 45 | 4 | ✗ | all | 1 | rational |
| 4.8.562 | 4 | 8 | 44 | 12 | ✗ | all | 1 | rational |
| 4.8.563 | 4 | 8 | 43 | 4 | ✗ | all but 2 | 0 | rational |
| 4.8.565 | 4 | 8 | 42 | 4 | ✗ | all | 5 | rational |
| 4.8.566 | 4 | 8 | 40 | 8 | ✗ | all | 4 | rational |
| 4.8.576 | 4 | 8 | 30 | 12 | ✗ | all | 4 | rational |
| 4.8.578 | 4 | 8 | 29 | 24 | ✗ | all | 3 | rational |
| 4.8.585 | 4 | 8 | 49 | 24 | ✓ | all | 2 | rational |
| 4.8.588 | 4 | 8 | 45 | 36 | ✓ | all | 2 | rational |
| 4.8.589 | 4 | 8 | 36 | 1152 | ✓ | all | 1 | rational |
| 4.8.597 | 4 | 8 | 43 | 4 | ✗ | all | 3 | rational |
| 4.8.598 | 4 | 8 | 42 | 24 | ✗ | all | 2 | rational |
| 4.8.599 | 4 | 8 | 39 | 12 | ✗ | all | 3 | rational |
| 4.8.603 | 4 | 8 | 37 | 16 | ✗ | all | 2 | rational |
| 4.8.604 | 4 | 8 | 36 | 48 | ✗ | all | 2 | rational |
| 4.8.609 | 4 | 8 | 28 | 6 | ✗ | all | 1 | rational |
| 4.8.610 | 4 | 8 | 27 | 72 | ✗ | all | 0 | rational |
| 4.8.637 | 4 | 8 | 48 | 24 | ✓ | all | 2 | rational |
| 4.8.639 | 4 | 8 | 45 | 144 | ✓ | all | 3 | rational |
| 4.8.640 | 4 | 8 | 45 | 24 | ✓ | all | 2 | rational |
| 4.8.641 | 4 | 8 | 36 | 144 | ✗ | all | 1 | rational |
| 4.8.659 | 4 | 8 | 47 | 4 | ✓ | all | 2 | rational |
| 4.8.661 | 4 | 8 | 46 | 12 | ✓ | all | 6 | rational |