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393 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.8.72 | 4 | 8 | 62 | 8 | ✓ | all | 1 | rational |
| 4.8.111 | 4 | 8 | 64 | 384 | ✓ | all | 4 | rational |
| 4.8.159 | 4 | 8 | 62 | 6 | ✓ | all | 2 | rational over Q(a)/(a^2 - a + 1) |
| 4.8.178 | 4 | 8 | 61 | 16 | ✓ | all | 2 | rational |
| 4.8.193 | 4 | 8 | 62 | 8 | ✓ | ∅ | -1 | empty |
| 4.8.210 | 4 | 8 | 60 | 16 | ✓ | all | 2 | empty |
| 4.8.214 | 4 | 8 | 60 | 64 | ✓ | all but 2 | 1 | rational |
| 4.8.228 | 4 | 8 | 61 | 2 | ✓ | all | 2 | point over Q(a)/(a^2 - a - 1) |
| 4.8.230 | 4 | 8 | 61 | 8 | ✓ | all | 1 | point over Q(a)/(a^2 - a + 1) |
| 4.8.263 | 4 | 8 | 60 | 24 | ✓ | ∅ | -1 | empty |
| 4.8.269 | 4 | 8 | 56 | 1344 | ✓ | ∅ | -1 | empty |
| 4.8.293 | 4 | 8 | 60 | 8 | ✓ | all but 2 | 2 | rational |
| 4.8.307 | 4 | 8 | 59 | 2 | ✓ | {2} | -1 | rational |
| 4.8.312 | 4 | 8 | 58 | 24 | ✓ | ∅ | -1 | empty |
| 4.8.316 | 4 | 8 | 57 | 24 | ✓ | all | 6 | rational |
| 4.8.320 | 4 | 8 | 52 | 96 | ✗ | all | 5 | rational |
| 4.8.324 | 4 | 8 | 60 | 720 | ✓ | all | 4 | rational |
| 4.8.358 | 4 | 8 | 59 | 2 | ✓ | all | 4 | rational |
| 4.8.360 | 4 | 8 | 60 | 8 | ✓ | all | 2 | rational |
| 4.8.366 | 4 | 8 | 58 | 24 | ✓ | all | 7 | empty |
| 4.8.369 | 4 | 8 | 57 | 24 | ✓ | all | 6 | rational |
| 4.8.374 | 4 | 8 | 58 | 8 | ✓ | all | 4 | rational |
| 4.8.376 | 4 | 8 | 56 | 8 | ✓ | all | 4 | rational |
| 4.8.377 | 4 | 8 | 50 | 240 | ✗ | all | 3 | rational |
| 4.8.385 | 4 | 8 | 54 | 144 | ✓ | all | 4 | rational |
| 4.8.394 | 4 | 8 | 58 | 2 | ✓ | all | 3 | rational |
| 4.8.408 | 4 | 8 | 58 | 6 | ✓ | all but 2 | 1 | rational |
| 4.8.416 | 4 | 8 | 58 | 2 | ✓ | all | 3 | rational |
| 4.8.420 | 4 | 8 | 57 | 1 | ✓ | all | 1 | rational |
| 4.8.423 | 4 | 8 | 57 | 2 | ✓ | all | 5 | rational |
| 4.8.426 | 4 | 8 | 57 | 2 | ✓ | all | 5 | rational |
| 4.8.428 | 4 | 8 | 56 | 6 | ✓ | all | 4 | point over Q(a)/(a^2 - a + 1) |
| 4.8.433 | 4 | 8 | 57 | 2 | ✓ | all | 4 | rational |
| 4.8.435 | 4 | 8 | 55 | 2 | ✓ | all | 4 | rational |
| 4.8.437 | 4 | 8 | 54 | 12 | ✓ | all | 3 | rational |
| 4.8.439 | 4 | 8 | 55 | 2 | ✓ | all | 4 | rational |
| 4.8.441 | 4 | 8 | 53 | 2 | ✓ | all | 3 | rational |
| 4.8.442 | 4 | 8 | 52 | 4 | ✓ | all | 2 | rational |
| 4.8.450 | 4 | 8 | 56 | 2 | ✓ | all | 2 | rational |
| 4.8.453 | 4 | 8 | 55 | 4 | ✓ | all | 4 | rational |
| 4.8.456 | 4 | 8 | 53 | 4 | ✓ | all | 3 | rational |
| 4.8.458 | 4 | 8 | 54 | 48 | ✓ | all | 3 | rational |
| 4.8.461 | 4 | 8 | 56 | 8 | ✓ | all | 3 | rational |
| 4.8.463 | 4 | 8 | 55 | 2 | ✓ | all | 2 | rational |
| 4.8.466 | 4 | 8 | 54 | 8 | ✓ | all | 2 | empty |
| 4.8.467 | 4 | 8 | 51 | 12 | ✓ | all | 1 | rational |
| 4.8.471 | 4 | 8 | 54 | 48 | ✓ | all | 1 | rational |
| 4.8.478 | 4 | 8 | 56 | 2 | ✓ | all | 3 | rational |
| 4.8.481 | 4 | 8 | 55 | 2 | ✓ | all | 3 | rational |
| 4.8.483 | 4 | 8 | 51 | 12 | ✓ | all | 2 | rational |