Database - av_fq_isog

Formats: - HTML - YAML - JSON - 2026-10-23T22:03:13.803727

Query: /api/av_fq_isog/?_offset=0

Table av_fq_isog

Isogeny classes of abelian varieties over finite fields

Column	Type	Example
abvar_count	numeric	374832
abvar_counts	numeric[]	[374832, 153169849152, 59609391125070528, 23283061948024753741056, 9094948321666761436331439792, 355...
abvar_counts_str	text	'374832 153169849152 59609391125070528 23283061948024753741056 9094948321666761436331439792 35527136...
all_polarized_product	boolean
all_unpolarized_product	boolean
angle_corank	smallint	0
angle_rank	smallint	2
angles	double precision[]	[0.282997954035343, 0.528731087631289]
center_dim	smallint	4
cohen_macaulay_max	smallint
curve_count	integer	599
curve_counts	numeric[]	[599, 392113, 244160066, 152587874785, 95367445313399, 59604644909297950, 37252902965224139015, 2328...
curve_counts_str	text	'599 392113 244160066 152587874785 95367445313399 59604644909297950 37252902965224139015 23283064364...
curves	text[]
dim1_distinct	smallint	0
dim1_factors	smallint	0
dim2_distinct	smallint	1
dim2_factors	smallint	1
dim3_distinct	smallint	0
dim3_factors	smallint	0
dim4_distinct	smallint	0
dim4_factors	smallint	0
dim5_distinct	smallint	0
dim5_factors	smallint	0
endomorphism_ring_count	smallint
g	smallint	2
galois_groups	text[]	['4T3']
geom_dim1_distinct	smallint	0
geom_dim1_factors	smallint	0
geom_dim2_distinct	smallint	1
geom_dim2_factors	smallint	1
geom_dim3_distinct	smallint	0
geom_dim3_factors	smallint	0
geom_dim4_distinct	smallint	0
geom_dim4_factors	smallint	0
geom_dim5_distinct	smallint	0
geom_dim5_factors	smallint	0
geometric_center_dim	smallint	4
geometric_extension_degree	smallint	1
geometric_galois_groups	text[]	['4T3']
geometric_number_fields	text[]	['4.0.1212872689.1']
geometric_splitting_field	text
geometric_splitting_polynomials	numeric[]	[[785, -222, 223, -2, 1]]
group_structure_count	smallint
has_geom_ss_factor	boolean	False
has_jacobian	smallint	1
has_principal_polarization	smallint	1
hyp_count	integer
is_cyclic	boolean	False
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	'2.625.abb_bqq'
max_divalg_dim	smallint	1
max_geom_divalg_dim	smallint	1
max_twist_degree	integer	2
newton_coelevation	smallint	2
newton_elevation	smallint	0
noncyclic_primes	integer[]	[2, 3]
number_fields	text[]	['4.0.1212872689.1']
p	smallint	5
p_rank	smallint	2
p_rank_deficit	smallint	0
pic_prime_gens	integer[]
poly	integer[]	[1, -27, 1108, -16875, 390625]
poly_str	text	'1 -27 1108 -16875 390625 '
primitive_models	text[]	[]
principal_polarization_count	integer
q	integer	625
real_poly	integer[]	[1, -27, -142]
simple_distinct	text[]	['2.625.abb_bqq']
simple_factors	text[]	['2.625.abb_bqqA']
simple_multiplicities	smallint[]	[1]
singular_primes	text[]
size	integer
slopes	text[]	['0A', '0B', '1A', '1B']
splitting_field	text
splitting_polynomials	numeric[]	[[785, -222, 223, -2, 1]]
twist_count	integer	2
twists	jsonb	[['2.625.bb_bqq', '2.390625.cff_ckltw', 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': 1764, 'abvar_counts': [1764, 4791024, 11112945984, 23770838052864, 51061275145729044, 112545842500773577728, 247048649933906588545764, 542829324362558189169475584, 1192545716443084177397568733248, 2619966600357079542346689297193584], 'abvar_counts_str': '1764 4791024 11112945984 23770838052864 51061275145729044 112545842500773577728 247048649933906588545764 542829324362558189169475584 1192545716443084177397568733248 2619966600357079542346689297193584 ', 'angle_corank': 0, 'angle_rank': 3, 'angles': [0.19626366619029, 0.355929670173224, 0.815779813676352], 'center_dim': 6, 'curve_count': 11, 'curve_counts': [11, 167, 2300, 29135, 370391, 4830692, 62744483, 815773631, 10604609852, 137856963647], 'curve_counts_str': '11 167 2300 29135 370391 4830692 62744483 815773631 10604609852 137856963647 ', 'curves': ['y^2=x^7+x^6+7*x^5+x^4+2*x^3+2*x^2+12*x+2', 'y^2=x^7+2*x^6+9*x^5+3*x^4+2*x^3+10*x^2+6*x+12', 'y^2=x^7+2*x^6+8*x^5+12*x^4+3*x^3+2*x^2+10*x+12', 'y^2=x^7+x^6+3*x^5+10*x^3+7*x^2+9*x+11', 'y^2=x^7+9*x^6+8*x^5+5*x^4+11*x^3+2*x^2+8*x+10', 'y^2=x^7+11*x^6+11*x^5+12*x^4+9*x^3+3*x^2+9*x+7', 'y^2=x^7+5*x^6+11*x^5+8*x^4+8*x^3+1', 'y^2=x^7+12*x^6+5*x^5+12*x^2+4*x+4', 'y^2=x^7+5*x^6+10*x^5+3*x^4+8*x^2+11*x+11', 'y^2=x^7+3*x^6+4*x^5+3*x^4+7*x^3+12*x^2+4*x+10', 'y^2=x^7+2*x^6+2*x^5+2*x^4+4*x^3+x^2+3*x+6', 'y^2=x^7+5*x^6+12*x^5+11*x^4+2*x^3+9*x+5', 'y^2=x^7+3*x^6+2*x^5+7*x^4+5*x^3+12*x+3', 'y^2=x^7+x^6+12*x^5+11*x^4+8*x^3+5*x^2+4*x+5', 'y^2=x^7+11*x^6+3*x^5+2*x^4+3*x^3+7*x^2+6*x+8', 'y^2=x^7+11*x^6+x^5+2*x^4+2*x^3+12*x^2+8*x+10', 'y^2=x^7+7*x^6+7*x^5+12*x^4+6*x^3+2*x^2+8*x+3', 'y^2=x^7+10*x^6+5*x^4+12*x^3+x^2+10*x+5', 'y^2=x^7+x^6+5*x^4+8*x^3+12*x+6', 'y^2=x^7+4*x^6+2*x^5+7*x^4+3*x^3+9*x^2+8*x+4', 'y^2=x^7+x^6+5*x^5+9*x^4+2*x^3+3*x^2+4*x+5', 'y^2=2*x^7+4*x^6+7*x^5+12*x^4+11*x^3+11*x^2+11*x+9', 'y^2=2*x^7+8*x^6+3*x^5+4*x^4+10*x^3+x^2+4*x+1', 'y^2=x^7+5*x^5+4*x^4+2*x^3+2*x^2+6*x+4', 'y^2=2*x^7+8*x^6+4*x^5+9*x^4+11*x^3+4*x^2+2', 'y^2=2*x^8+5*x^7+11*x^6+9*x^5+8*x^4+5*x^3+7*x', 'y^2=x^8+11*x^7+11*x^6+6*x^5+7*x^4+12*x^3+2*x^2+x+1', 'y^2=2*x^8+11*x^7+x^6+7*x^5+11*x^4+6*x^3+x^2+12*x+10', 'y^2=x^8+11*x^7+3*x^6+11*x^5+10*x^4+12*x^3+3*x^2+12*x+9', 'y^2=2*x^8+9*x^7+6*x^6+8*x^5+4*x^3+10*x+12', 'y^2=2*x^8+4*x^7+6*x^6+9*x^4+4*x^3+x^2+6*x+11', 'y^2=x^8+5*x^7+x^6+10*x^4+7*x^3+7*x^2+4*x+11', 'y^2=2*x^8+4*x^7+2*x^6+11*x^5+7*x^4+5*x^3+9*x^2+4*x+11', 'y^2=2*x^8+9*x^7+2*x^6+3*x^5+4*x^4+7*x^3+4*x^2+9*x+1', 'y^2=2*x^8+6*x^7+11*x^6+7*x^5+5*x^4+x^3+6*x^2+12*x+11', 'y^2=x^8+3*x^7+7*x^6+11*x^5+5*x^4+5*x^3+9*x^2+5*x+11', 'y^2=2*x^8+6*x^7+8*x^6+12*x^5+4*x^4+7*x^3+12*x^2+10*x+7', 'y^2=x^8+10*x^7+5*x^6+12*x^5+12*x^4+8*x^3+4*x+8', 'y^2=x^8+10*x^7+11*x^6+10*x^4+4*x^2+12*x+11', 'y^2=2*x^8+9*x^7+10*x^6+11*x^5+11*x^4+x^3+12*x^2+6', 'y^2=x^8+x^7+7*x^6+12*x^5+5*x^4+5*x^3+4*x^2+8*x+2', 'y^2=2*x^8+8*x^7+7*x^6+2*x^5+5*x^4+6*x^3+8*x^2+10*x+6', 'y^2=2*x^8+2*x^7+8*x^5+x^4+6*x^3+9*x^2+7*x+11'], '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': ['6.0.487450224.1'], 'geometric_splitting_field': '6.0.487450224.1', 'geometric_splitting_polynomials': [[79, 0, 90, 0, 18, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 43, 'id': 1339671, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'label': '3.13.ad_d_bi', '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': ['6.0.487450224.1'], 'p': 13, 'p_rank': 3, 'p_rank_deficit': 0, 'poly': [1, -3, 3, 34, 39, -507, 2197], 'poly_str': '1 -3 3 34 39 -507 2197 ', 'primitive_models': [], 'q': 13, 'real_poly': [1, -3, -36, 112], 'simple_distinct': ['3.13.ad_d_bi'], 'simple_factors': ['3.13.ad_d_biA'], 'simple_multiplicities': [1], 'slopes': ['0A', '0B', '0C', '1A', '1B', '1C'], 'splitting_field': '6.0.487450224.1', 'splitting_polynomials': [[79, 0, 90, 0, 18, 0, 1]], 'twist_count': 2, 'twists': [['3.13.d_d_abi', '3.169.ad_lf_qo', 2]]}