Database - av_fq_isog

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Table av_fq_isog

Isogeny classes of abelian varieties over finite fields

Column	Type	Example
abvar_count	numeric	4618
abvar_counts	numeric[]	[4618, 54593996, 326361896746, 2196499458154592, 15182762481360045088, 104208320763357207781004, 714...
abvar_counts_str	text	'4618 54593996 326361896746 2196499458154592 15182762481360045088 104208320763357207781004 714299777...
all_polarized_product	boolean
all_unpolarized_product	boolean
angle_corank	smallint	0
angle_rank	smallint	3
angles	double precision[]	[0.164122803220251, 0.456233928491464, 0.49194117205416]
center_dim	smallint	6
cohen_macaulay_max	smallint
curve_count	integer	11
curve_counts	numeric[]	[11, 417, 6935, 129329, 2476366, 47082453, 893984725, 16983333969, 322686449213, 6131069889992]
curve_counts_str	text	'11 417 6935 129329 2476366 47082453 893984725 16983333969 322686449213 6131069889992 '
curves	text[]	['y^2=18*x^8+4*x^7+18*x^6+9*x^5+2*x^4+8*x^3+9*x^2+17*x+3', 'y^2=x^8+16*x^7+7*x^6+7*x^5+6*x^4+16*x^3+...
dim1_distinct	smallint	0
dim1_factors	smallint	0
dim2_distinct	smallint	0
dim2_factors	smallint	0
dim3_distinct	smallint	1
dim3_factors	smallint	1
dim4_distinct	smallint	0
dim4_factors	smallint	0
dim5_distinct	smallint	0
dim5_factors	smallint	0
endomorphism_ring_count	smallint
g	smallint	3
galois_groups	text[]	['6T11']
geom_dim1_distinct	smallint	0
geom_dim1_factors	smallint	0
geom_dim2_distinct	smallint	0
geom_dim2_factors	smallint	0
geom_dim3_distinct	smallint	1
geom_dim3_factors	smallint	1
geom_dim4_distinct	smallint	0
geom_dim4_factors	smallint	0
geom_dim5_distinct	smallint	0
geom_dim5_factors	smallint	0
geometric_center_dim	smallint	6
geometric_extension_degree	smallint	1
geometric_galois_groups	text[]	['6T11']
geometric_number_fields	text[]	['6.0.461937306248.1']
geometric_splitting_field	text	'6.0.461937306248.1'
geometric_splitting_polynomials	numeric[]	[[3641, 561, 380, 0, 38, -3, 1]]
group_structure_count	smallint
has_geom_ss_factor	boolean	False
has_jacobian	smallint	1
has_principal_polarization	smallint	1
hyp_count	integer	5
is_cyclic	boolean	True
is_geometrically_simple	boolean	True
is_geometrically_squarefree	boolean	True
is_primitive	boolean	True
is_simple	boolean	True
is_squarefree	boolean	True
is_supersingular	boolean	False
jacobian_count	integer
label	text	'3.19.aj_cq_ang'
max_divalg_dim	smallint	1
max_geom_divalg_dim	smallint	1
max_twist_degree	integer	2
newton_coelevation	smallint	4
newton_elevation	smallint	0
noncyclic_primes	integer[]	[]
number_fields	text[]	['6.0.461937306248.1']
p	smallint	19
p_rank	smallint	3
p_rank_deficit	smallint	0
pic_prime_gens	integer[]
poly	integer[]	[1, -9, 68, -344, 1292, -3249, 6859]
poly_str	text	'1 -9 68 -344 1292 -3249 6859 '
primitive_models	text[]	[]
principal_polarization_count	integer
q	integer	19
real_poly	integer[]	[1, -9, 11, -2]
simple_distinct	text[]	['3.19.aj_cq_ang']
simple_factors	text[]	['3.19.aj_cq_angA']
simple_multiplicities	smallint[]	[1]
singular_primes	text[]
size	integer
slopes	text[]	['0A', '0B', '0C', '1A', '1B', '1C']
splitting_field	text	'6.0.461937306248.1'
splitting_polynomials	numeric[]	[[3641, 561, 380, 0, 38, -3, 1]]
twist_count	integer	2
twists	jsonb	[['3.19.j_cq_ng', '3.361.cd_bnc_src', 2]]
weak_equivalence_count	smallint
zfv_index	numeric
zfv_index_factorization	numeric[]
zfv_is_bass	boolean
zfv_is_maximal	boolean
zfv_pic_size	integer
zfv_plus_index	numeric
zfv_plus_index_factorization	numeric[]
zfv_plus_norm	numeric
zfv_singular_count	smallint
zfv_singular_primes	text[]

{'abvar_count': 1908, 'abvar_counts': [1908, 2129328, 2325844368, 3205268921088, 4178084422166748, 5557529759978476800, 7394128767792923511492, 9849108429597196005322752, 13111172066244525314817603888, 17449237108803346943338852212528], 'abvar_counts_str': '1908 2129328 2325844368 3205268921088 4178084422166748 5557529759978476800 7394128767792923511492 9849108429597196005322752 13111172066244525314817603888 17449237108803346943338852212528 ', 'angle_corank': 0, 'angle_rank': 3, 'angles': [0.298489733980124, 0.586722556015653, 0.782147048426464], 'center_dim': 6, 'curve_count': 15, 'curve_counts': [15, 143, 1314, 14951, 161085, 1770800, 19471047, 214345295, 2358159534, 25937179103], 'curve_counts_str': '15 143 1314 14951 161085 1770800 19471047 214345295 2358159534 25937179103 ', 'curves': ['y^2=4*x^8+9*x^7+x^6+2*x^4+2*x^3+6*x+8', 'y^2=3*x^8+4*x^7+4*x^6+5*x^5+3*x^4+5*x^3+10*x^2+4*x+2', 'y^2=2*x^8+x^7+x^6+4*x^5+9*x^4+4*x^2+4', 'y^2=x^8+7*x^7+9*x^6+3*x^5+8*x^4+3*x^3+3*x^2+8*x+5', 'y^2=10*x^8+8*x^7+10*x^6+10*x^5+x^4+3*x^3+x^2+8*x+10', 'y^2=x^8+8*x^7+4*x^6+7*x^5+7*x^4+x^2+4*x+2', 'y^2=9*x^8+5*x^7+6*x^6+4*x^5+4*x^4+5*x^3+2*x^2+6*x+7', 'y^2=x^8+10*x^7+3*x^6+8*x^5+5*x^4+7*x^3+8*x^2+2*x+2', 'y^2=x^8+4*x^6+x^5+9*x^4+5*x^3+9*x^2+3*x+3', 'y^2=6*x^8+x^7+3*x^6+6*x^4+8*x^3+8*x^2+2*x+3', 'y^2=3*x^8+4*x^7+2*x^6+4*x^5+3*x^3+9*x^2+8*x+3', 'y^2=3*x^8+7*x^7+5*x^4+8*x^3+9*x^2+6*x+4', 'y^2=5*x^8+x^7+2*x^6+4*x^5+8*x^4+4*x^3+10*x^2+10*x+2', 'y^2=4*x^8+3*x^7+7*x^5+9*x^4+3*x^3+10*x^2+4*x+1', 'y^2=10*x^8+4*x^7+3*x^6+5*x^4+3*x^3+2*x^2+2*x+8', 'y^2=5*x^8+10*x^7+3*x^6+x^5+3*x^4+9*x^3+5*x^2+9*x+9', 'y^2=6*x^8+5*x^7+3*x^6+9*x^5+2*x^4+3*x^3+5*x^2+x+3', 'y^2=4*x^8+8*x^7+x^5+2*x^4+9*x^3+2*x^2+8*x', 'y^2=3*x^8+9*x^7+9*x^6+4*x^5+3*x^4+9*x^3+10*x^2+3*x+5', 'y^2=4*x^7+5*x^6+6*x^5+4*x^4+x^3+10*x^2+5*x+10', 'y^2=x^7+3*x^6+5*x^5+6*x^3+2*x^2+5*x+8', 'y^2=10*x^8+10*x^7+10*x^6+4*x^5+7*x^4+5*x^3+2*x+3', 'y^2=7*x^7+5*x^6+9*x^5+9*x^4+5*x^3+3*x^2+9*x+3', 'y^2=5*x^8+9*x^7+2*x^6+2*x^5+8*x^4+x^3+3*x^2+x+5', 'y^2=2*x^8+10*x^7+3*x^6+10*x^5+8*x^4+8*x^3+8*x^2+2*x+2', 'y^2=3*x^8+7*x^7+3*x^6+9*x^5+7*x^3+7*x^2+4*x+6', 'y^2=9*x^8+4*x^7+6*x^6+3*x^5+5*x^4+5*x^3+x^2+8*x+10', 'y^2=10*x^8+9*x^7+8*x^6+8*x^5+10*x^4+6*x^2+x+4', 'y^2=4*x^8+4*x^7+5*x^6+9*x^5+6*x^4+9*x^3+3*x^2+9*x', 'y^2=2*x^7+x^6+5*x^5+3*x^4+10*x^3+5*x^2+5*x+5', 'y^2=x^8+x^7+8*x^6+2*x^5+4*x^4+10*x^3+9*x^2+4*x+5', 'y^2=x^8+5*x^7+5*x^6+7*x^5+10*x^4+2*x^3+8*x^2+5', 'y^2=2*x^8+3*x^7+9*x^6+10*x^5+7*x^3+6*x^2+6*x+10', 'y^2=6*x^7+5*x^6+10*x^3+9*x+5', 'y^2=9*x^8+5*x^7+10*x^6+8*x^5+10*x^3+x^2+5*x+4', 'y^2=8*x^8+2*x^7+8*x^6+9*x^5+5*x^4+6*x^3+2*x+10', 'y^2=x^8+4*x^7+10*x^6+7*x^5+8*x^4+4*x^3+2*x^2+7*x+2', 'y^2=4*x^8+2*x^7+6*x^6+3*x^5+9*x^4+7*x^3+4*x^2+7*x+2'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 1, 'dim3_factors': 1, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 3, 'galois_groups': ['6T11'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 1, 'geom_dim3_factors': 1, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 6, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['6T11'], 'geometric_number_fields': ['6.0.14381280432.1'], 'geometric_splitting_field': '6.0.14381280432.1', 'geometric_splitting_polynomials': [[761, 15, 156, -9, 18, -3, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 38, 'id': 1319785, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'label': '3.11.d_p_be', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 4, 'newton_elevation': 0, 'noncyclic_primes': [2, 3], 'number_fields': ['6.0.14381280432.1'], 'p': 11, 'p_rank': 3, 'p_rank_deficit': 0, 'poly': [1, 3, 15, 30, 165, 363, 1331], 'poly_str': '1 3 15 30 165 363 1331 ', 'primitive_models': [], 'q': 11, 'real_poly': [1, 3, -18, -36], 'simple_distinct': ['3.11.d_p_be'], 'simple_factors': ['3.11.d_p_beA'], 'simple_multiplicities': [1], 'slopes': ['0A', '0B', '0C', '1A', '1B', '1C'], 'splitting_field': '6.0.14381280432.1', 'splitting_polynomials': [[761, 15, 156, -9, 18, -3, 1]], 'twist_count': 2, 'twists': [['3.11.ad_p_abe', '3.121.v_ol_gsk', 2]]}