Matroid database
Search
Statistics
Search
Size
rank
n
Invariants
Bases
Automorphisms
Dimension of realization space
Girth
Expected dimension over ℤ
Realizability
realizable
any
yes
no
unknown
in char 0
any
yes
no
unknown
realizable in characteristic
char set class
any
cofinite
finite
empty
unknown
birational type
any
unknown
rational
empty
rational over Q(a)/(a^2 - a + 1)
point over Q(a)/(a^3 - a^2 + 1)
genus 1 curve (11a3)
point over Q(a)/(a^2 - a - 1)
point over Q(a)/(a^2 - a + 1)
point over Q(a)/(a^2 + 1)
point over Q(a)/(a^2 - 2)
rational over Q(a)/(a^2 - a - 1)
K3 surface
genus 1 curve (14a4)
genus 1 curve (15a8)
point over Q(a)/(a^2 - a + 2)
rational over Q(a)/(a^2 + 1)
curve of genus 2
point over Q(a)/(a^3 + a - 1)
genus 1 curve (37a1)
point over Q(a)/(a^3 - a^2 + a + 1)
point over Q(a)/(a^3 - a^2 - 2*a + 1)
point over Q(a)/(a^4 - a^3 - a^2 + a + 1)
genus 1 curve (17a4)
rational over Q(a)/(a^3 - a^2 + 1)
point over Q(a)/(a^2 - 3)
genus 1 curve (43a1)
point over Q(a)/(a^4 - a - 1)
genus 1 curve (20a2)
genus 1 curve (11a3) x P^1
point over Q(a)/(a^2 - a - 4)
genus 1 curve (53a1)
point over Q(a)/(a^4 - a^3 + a^2 - a + 1)
genus 1 curve (19a3)
rational over Q(a)/(a^2 - 2)
point over Q(a)/(a^4 - a^3 + 2*a - 1)
genus 1 curve (58a1)
point over Q(a)/(a^3 + 2*a - 1)
point over Q(a)/(a^2 + 2)
point over Q(a)/(a^4 + a^2 - a + 1)
point over Q(a)/(a^4 - a^3 + a^2 + a - 1)
point over Q(a)/(a^4 - a^2 + 1)
genus 1 curve (65a1)
curve of genus 3
K3 surface x P^1
point over Q(a)/(a^3 - a - 2)
genus 1 curve (14a4) x P^1
genus 1 curve (24a4)
point over Q(a)/(a^4 - a^3 + 2*a + 1)
point over Q(a)/(a^3 - 2*a - 2)
point over Q(a)/(a^3 - 3*a - 1)
Calabi-Yau threefold (elliptic over P^1 x P^1, K trivial; kappa = 0, not rational)
point over Q(a)/(a^5 - a^3 - a^2 + a + 1)
genus 1 curve (27a3)
genus 1 curve (15a8) x P^1
ruled over the genus 1 curve 11a3
genus 1 curve
rational over Q(a)/(a^2 - a + 2)
point over Q(a)/(a^5 - a^4 + a^2 - a + 1)
genus 1 curve (37a1) x P^1
genus 1 curve (61a1)
point over Q(a)/(a^4 + 1)
rational over Q(a)/(a^3 - a^2 + a + 1)
point over Q(a)/(a^5 - a^4 + a^3 - 2*a^2 + a - 1)
genus 1 curve (21a4)
point over Q(a)/(a^4 - a + 1)
point over Q(a)/(a^3 - a^2 - 2)
genus 1 curve (57a1)
point over Q(a)/(a^3 - a^2 - 3*a + 1)
point over Q(a)/(a^4 - a^3 - a^2 + 3*a - 1)
point over Q(a)/(a^4 - 2*a - 1)
point over Q(a)/(a^4 - 2*a^3 + 2)
point over Q(a)/(a^2 - a - 3)
point over Q(a)/(a^4 - a^3 - a^2 - a + 1)
rational over Q(a)/(a^3 - a^2 - 2*a + 1)
genus 1 curve (92b1)
genus 1 curve (32a2)
point over Q(a)/(a^2 - a + 4)
genus 1 curve (34a1)
point over Q(a)/(a^4 - a^3 + a^2 - a - 1)
genus 1 curve (26b1)
point over Q(a)/(a^4 - a^3 - 3*a^2 + a + 1)
rational over Q(a)/(a^4 - a^3 + a^2 - a + 1)
genus 1 curve (79a1)
ruled over the genus 1 curve 15a8
point over Q(a)/(a^5 - 2*a^4 + 2*a^3 - a^2 + 1)
genus 1 curve (101a1)
genus 1 curve (38b1)
genus 1 curve (82a1)
genus 1 curve (11a3) x P^2
point over Q(a)/(a^4 - 2*a^3 + a^2 - a - 1)
genus 1 curve (89a1)
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(0,-1) - 0E (rationality undetermined)
point over Q(a)/(a^4 - a^3 + a + 1)
point over Q(a)/(a^4 - 2*a^3 + a^2 - 2*a + 1)
point over Q(a)/(a^2 - a - 8)
genus 1 curve (36a1)
point over Q(a)/(a^3 - 2)
point over Q(a)/(a^4 - a^2 - 1)
point over Q(a)/(a^3 - a^2 + a - 2)
point over Q(a)/(a^5 - a^3 - 2*a^2 + 1)
genus 1 curve (83a1)
point over Q(a)/(a^3 - a^2 - 2*a - 2)
genus 1 curve (26a3)
genus 1 curve (124a1)
point over Q(a)/(a^3 - a^2 + 2*a + 1)
point over Q(a)/(a^5 - a^4 + a^3 - a^2 - 1)
genus 1 curve (102a1)
K3 surface x P^2
genus 1 curve (24a1)
genus 1 curve (35a3)
genus 1 curve (39a4)
point over Q(a)/(a^5 - a^4 + a^3 - a^2 + 2*a - 1)
point over Q(a)/(a^5 + a^3 - 2*a^2 - 1)
point over Q(a)/(a^4 + 2*a^2 - 2*a + 1)
genus 1 curve (131a1)
genus 1 curve (62a1)
genus 1 curve (99a1)
curve of genus 4
point over Q(a)/(a^6 - a^5 - a^2 + a + 1)
ruled over the genus 1 curve 14a4
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(-1,-1) - 0E (rationality undetermined)
point over Q(a)/(a^2 - 7)
point over Q(a)/(a^5 + 2*a^3 - a^2 + 2*a - 1)
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(0,0) - 1E (rationality undetermined)
point over Q(a)/(a^6 - a^5 + 2*a^4 - 2*a^3 + 2*a^2 - 2*a + 1)
genus 1 curve (40a3)
genus 1 curve (14a4) x P^2
genus 1 curve (155c1)
point over Q(a)/(a^5 - a^4 - a^3 + 2*a^2 - a - 1)
genus 1 curve (15a8) x P^2
point over Q(a)/(a^4 - 2*a^2 - 1)
point over Q(a)/(a^5 - a^4 - a^3 + 3*a^2 - 1)
genus 1 curve (42a1)
point over Q(a)/(a^4 - a^3 + 2*a^2 - 2*a + 2)
point over Q(a)/(a^3 - a^2 - 4*a + 2)
point over Q(a)/(a^3 - a^2 + a - 3)
point over Q(a)/(a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)
point over Q(a)/(a^5 - a^2 - 1)
point over Q(a)/(a^5 - a^4 + 2*a^2 - a + 1)
genus 1 curve (37a1) x P^2
point over Q(a)/(a^5 - 2*a^2 - 2*a - 1)
ruled over the genus 1 curve 37a1
point over Q(a)/(a^5 + a^3 - 2*a^2 - a - 1)
point over Q(a)/(a^5 - a^4 - a^3 + 2*a + 1)
point over Q(a)/(a^4 - a^3 - 2*a^2 - a + 1)
point over Q(a)/(a^5 - a^4 + a + 1)
genus 1 curve (389a1)
point over Q(a)/(a^4 - 2*a^3 + 5*a^2 - 4*a + 2)
point over Q(a)/(a^5 - 2*a^2 - 1)
point over Q(a)/(a^4 - a^2 - 3*a - 1)
point over Q(a)/(a^5 - 2*a^4 + 2*a^3 - 2*a + 2)
point over Q(a)/(a^4 - 2*a^3 + a^2 - 2)
point over Q(a)/(a^6 + 2*a^4 - a^3 + 2*a^2 + 1)
genus 1 curve (55a4)
point over Q(a)/(a^7 - a^5 - 2*a^4 + a^3 + 2*a^2 - a - 1)
point over Q(a)/(a^6 - a^5 - a^4 + 2*a^3 - a + 1)
genus 1 curve (118a1)
genus 1 curve (141d1)
genus 1 curve (48a4)
point over Q(a)/(a^6 - a^5 - 2*a^4 + 2*a^3 - 2*a + 1)
point over Q(a)/(a^6 - 2*a^4 - a^3 + 2*a + 1)
genus 1 curve (158a1)
genus 1 curve (91b1)
point over Q(a)/(a^6 - a^5 + 4*a^3 - 2*a^2 - 2*a + 1)
point over Q(a)/(a^6 - a^5 + a^4 + 2*a^3 - 4*a^2 + 3*a - 1)
point over Q(a)/(a^6 - a^5 - a - 1)
point over Q(a)/(a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)
point over Q(a)/(a^4 - 2*a^3 - 2*a + 1)
point over Q(a)/(a^4 - a^3 + 2*a^2 - a + 2)
point over Q(a)/(a^6 - 2*a^5 + 2*a^4 - 2*a^2 + 3*a - 1)
point over Q(a)/(a^5 + a^3 + a - 1)
genus 1 curve (15a3)
point over Q(a)/(a^5 - 2*a^4 + 2*a^3 - 2*a^2 - 1)
genus 1 curve x P^1
point over Q(a)/(a^5 - a^4 + 2*a^3 - a^2 + 1)
point over Q(a)/(a^5 - a^4 + 2*a^3 - a^2 + 2*a - 1)
genus 1 curve (433a1)
point over Q(a)/(a^5 - 2*a^4 + a^3 + 2*a^2 - 2*a - 1)
point over Q(a)/(a^4 - 2*a^3 - a^2 + 2*a + 2)
point over Q(a)/(a^4 - 4*a^2 + 1)
point over Q(a)/(a^4 - a^3 - 2*a^2 + 3)
point over Q(a)/(a^3 - a^2 - 4*a - 1)
point over Q(a)/(a^6 - a^5 + a^4 - 2*a^2 + a - 1)
point over Q(a)/(a^4 - a^2 - 2*a + 1)
genus 1 curve (88a1)
point over Q(a)/(a^2 - a + 6)
point over Q(a)/(a^6 - a^5 + 2*a^4 - 3*a^3 + 2*a^2 - a + 1)
point over Q(a)/(a^5 - a^4 - 4*a^2 + 3*a + 2)
point over Q(a)/(a^5 - a - 1)
point over Q(a)/(a^3 - a^2 + 4*a - 2)
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(-1,0) - 0E (rationality undetermined)
genus 1 curve (196a1)
Properties
Simple
any
yes
no
unknown
Connected
any
yes
no
unknown
Paving
any
yes
no
unknown
Uniform
any
yes
no
unknown
Regular
any
yes
no
unknown
Binary
any
yes
no
unknown
Ternary
any
yes
no
unknown
Quaternary
any
yes
no
unknown
Graphic
any
yes
no
unknown
Transversal
any
yes
no
unknown
Series parallel
any
yes
no
unknown
Self dual
any
yes
no
unknown
Orientable
any
yes
no
unknown
Supersolvable
any
yes
no
unknown
Three lines
any
yes
no
unknown
Free realization space
any
yes
no
unknown
Realization space: smooth over ℤ
any
yes
no
unknown
Realization space: is regular scheme
any
yes
no
unknown
Search
reset
3,131 matroids, showing 1,401–1,450
label
▲
rank
⇅
n
⇅
#bases
⇅
#automorphisms
⇅
simple
⇅
char set
⇅
rs dim
⇅
birational type
⇅
3.12.9729042
3
12
202
1
✓
all
9
?
3.12.9862153
3
12
204
1
✓
all
9
?
3.12.10114079
3
12
204
1
✓
all
9
?
3.12.10207564
3
12
207
1
✓
all
9
?
3.12.10272191
3
12
204
1
✓
all
9
?
3.12.10393400
3
12
205
1
✓
all
9
?
3.12.10393406
3
12
204
1
✓
all
9
?
3.12.10393463
3
12
205
1
✓
all
9
?
3.12.10393693
3
12
206
1
✓
all
9
?
3.12.10393796
3
12
206
1
✓
all
9
?
3.12.10393962
3
12
205
1
✓
all
9
?
3.12.10394390
3
12
207
1
✓
all
9
?
3.12.10394658
3
12
204
1
✓
all
9
?
3.12.10396842
3
12
205
1
✓
all
9
?
3.12.10514079
3
12
205
1
✓
all
9
?
3.12.10625703
3
12
202
1
✓
all
9
?
3.12.11031483
3
12
206
1
✓
all
9
?
3.12.11150061
3
12
203
1
✓
all
9
?
3.12.11728411
3
12
204
1
✓
all
9
?
3.12.11764548
3
12
205
1
✓
all
9
?
3.12.11971924
3
12
204
1
✓
all
9
?
3.12.12336307
3
12
204
1
✓
all
9
?
3.12.12654228
3
12
202
1
✓
all
9
?
3.12.13334990
3
12
202
1
✓
all
9
?
3.12.13334992
3
12
204
1
✓
all
9
?
3.12.13335043
3
12
203
1
✓
all
9
?
3.12.13335283
3
12
203
1
✓
all
9
?
3.12.13362331
3
12
204
1
✓
all but 2
9
?
3.12.13362395
3
12
204
1
✓
all but 2
9
?
3.12.13364442
3
12
201
1
✓
all but 2
9
?
3.12.13553414
3
12
204
1
✓
all
9
?
3.12.13553419
3
12
205
1
✓
all
9
?
3.12.13553423
3
12
204
1
✓
all
9
?
3.12.13553429
3
12
205
1
✓
all
9
?
3.12.13553998
3
12
204
1
✓
all
9
?
3.12.13554103
3
12
203
1
✓
all
9
?
3.12.13554504
3
12
203
1
✓
all
9
?
3.12.13554534
3
12
202
1
✓
all
9
?
3.12.13554585
3
12
202
1
✓
all
9
?
3.12.13554664
3
12
202
1
✓
all
9
?
3.12.13554675
3
12
204
1
✓
all
9
?
3.12.13554868
3
12
204
1
✓
all
9
?
3.12.13555094
3
12
207
1
✓
all
9
?
3.12.13555392
3
12
206
1
✓
all
9
?
3.12.13557253
3
12
203
1
✓
all
9
?
3.12.13558355
3
12
204
1
✓
all
9
?
3.12.13558412
3
12
203
1
✓
all
9
?
3.12.13559063
3
12
205
1
✓
all
9
?
3.12.13771582
3
12
201
1
✓
all
9
?
3.12.13793871
3
12
205
1
✓
all but 2
9
?
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