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70 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.7.10 | 4 | 7 | 30 | ? | ✓ | all | 1 | rational |
| 4.7.12 | 4 | 7 | 29 | ? | ✓ | all but 2 | 0 | rational |
| 4.7.18 | 4 | 7 | 28 | ? | ✓ | all | 1 | rational |
| 4.7.19 | 4 | 7 | 27 | ? | ✓ | all | 2 | rational |
| 4.7.29 | 4 | 7 | 27 | ? | ✓ | all | 2 | rational |
| 4.7.31 | 4 | 7 | 26 | ? | ✓ | all | 1 | rational |
| 4.7.32 | 4 | 7 | 24 | ? | ✓ | all | 1 | rational |
| 4.7.34 | 4 | 7 | 24 | ? | ✓ | all | 1 | rational |
| 4.7.36 | 4 | 7 | 25 | ? | ✓ | all | 1 | rational |
| 4.7.37 | 4 | 7 | 24 | ? | ✓ | all | 0 | rational |
| 4.7.38 | 4 | 7 | 23 | ? | ✓ | all | 1 | rational |
| 4.7.39 | 4 | 7 | 21 | ? | ✓ | all | 0 | rational |
| 4.7.40 | 4 | 7 | 20 | ? | ✓ | all | 0 | rational |
| 4.7.42 | 4 | 7 | 22 | ? | ✗ | all | 1 | rational |
| 4.7.43 | 4 | 7 | 21 | ? | ✗ | all | 1 | rational |
| 4.7.44 | 4 | 7 | 20 | ? | ✗ | all | 0 | rational |
| 4.7.45 | 4 | 7 | 21 | ? | ✗ | all | 1 | rational |
| 4.7.46 | 4 | 7 | 18 | ? | ✗ | all | 1 | rational |
| 4.7.47 | 4 | 7 | 19 | ? | ✗ | all | 0 | rational |
| 4.7.48 | 4 | 7 | 16 | ? | ✗ | all | 0 | rational |
| 4.7.50 | 4 | 7 | 13 | ? | ✗ | all | 1 | rational |
| 4.7.51 | 4 | 7 | 12 | ? | ✗ | all | 0 | rational |
| 4.7.53 | 4 | 7 | 21 | ? | ✓ | all | 1 | rational |
| 4.7.54 | 4 | 7 | 18 | ? | ✓ | all | 1 | rational |
| 4.7.55 | 4 | 7 | 19 | ? | ✗ | all | 1 | rational |
| 4.7.56 | 4 | 7 | 18 | ? | ✗ | all | 0 | rational |
| 4.7.57 | 4 | 7 | 17 | ? | ✗ | all | 0 | rational |
| 4.7.58 | 4 | 7 | 15 | ? | ✗ | all | 0 | rational |
| 4.7.59 | 4 | 7 | 16 | ? | ✗ | all | 0 | rational |
| 4.7.60 | 4 | 7 | 14 | ? | ✗ | all | 0 | rational |
| 4.7.61 | 4 | 7 | 12 | ? | ✗ | all | 0 | rational |
| 4.7.62 | 4 | 7 | 12 | ? | ✗ | all | 1 | rational |
| 4.7.63 | 4 | 7 | 11 | ? | ✗ | all | 0 | rational |
| 4.7.64 | 4 | 7 | 9 | ? | ✗ | all | 0 | rational |
| 4.7.65 | 4 | 7 | 13 | ? | ✗ | all | 0 | rational |
| 4.7.66 | 4 | 7 | 12 | ? | ✗ | all | 0 | rational |
| 4.7.67 | 4 | 7 | 9 | ? | ✗ | all | 0 | rational |
| 4.7.68 | 4 | 7 | 8 | ? | ✗ | all | 0 | rational |
| 4.7.69 | 4 | 7 | 5 | ? | ✗ | all | 0 | rational |
| 4.7.72 | 4 | 7 | 18 | ? | ✓ | all | 2 | rational |
| 4.7.74 | 4 | 7 | 17 | ? | ✓ | all | 1 | rational |
| 4.7.75 | 4 | 7 | 16 | ? | ✓ | all | 0 | rational |
| 4.7.77 | 4 | 7 | 15 | ? | ✗ | all | 1 | rational |
| 4.7.80 | 4 | 7 | 15 | ? | ✓ | all | 1 | rational |
| 4.7.81 | 4 | 7 | 12 | ? | ✗ | all | 1 | rational |
| 4.7.82 | 4 | 7 | 14 | ? | ✗ | all | 1 | rational |
| 4.7.83 | 4 | 7 | 13 | ? | ✗ | all | 0 | rational |
| 4.7.84 | 4 | 7 | 12 | ? | ✗ | all | 0 | rational |
| 4.7.85 | 4 | 7 | 12 | ? | ✗ | all | 0 | rational |
| 4.7.86 | 4 | 7 | 10 | ? | ✗ | all | 0 | rational |