LMFDB - Abelian variety isogeny class data

Formats: - HTML - YAML - JSON - 2026-09-12T01:19:25.893787

Column	Type
abvar_count	numeric
abvar_counts	numeric[]
abvar_counts_str	text
all_polarized_product	boolean
all_unpolarized_product	boolean
angle_corank	smallint
angle_rank	smallint
angles	double precision[]
center_dim	smallint
cohen_macaulay_max	smallint
curve_count	integer
curve_counts	numeric[]
curve_counts_str	text
curves	text[]
dim1_distinct	smallint
dim1_factors	smallint
dim2_distinct	smallint
dim2_factors	smallint
dim3_distinct	smallint
dim3_factors	smallint
dim4_distinct	smallint
dim4_factors	smallint
dim5_distinct	smallint
dim5_factors	smallint
endomorphism_ring_count	smallint
g	smallint
galois_groups	text[]
geom_dim1_distinct	smallint
geom_dim1_factors	smallint
geom_dim2_distinct	smallint
geom_dim2_factors	smallint
geom_dim3_distinct	smallint
geom_dim3_factors	smallint
geom_dim4_distinct	smallint
geom_dim4_factors	smallint
geom_dim5_distinct	smallint
geom_dim5_factors	smallint
geometric_center_dim	smallint
geometric_extension_degree	smallint
geometric_galois_groups	text[]
geometric_number_fields	text[]
geometric_splitting_field	text
geometric_splitting_polynomials	numeric[]
group_structure_count	smallint
has_geom_ss_factor	boolean
has_jacobian	smallint
has_principal_polarization	smallint
hyp_count	integer
is_cyclic	boolean
is_geometrically_simple	boolean
is_geometrically_squarefree	boolean
is_primitive	boolean
is_simple	boolean
is_squarefree	boolean
is_supersingular	boolean
jacobian_count	integer
label	text
max_divalg_dim	smallint
max_geom_divalg_dim	smallint
max_twist_degree	integer
newton_coelevation	smallint
newton_elevation	smallint
noncyclic_primes	integer[]
number_fields	text[]
p	smallint
p_rank	smallint
p_rank_deficit	smallint
pic_prime_gens	integer[]
poly	integer[]
poly_str	text
primitive_models	text[]
principal_polarization_count	integer
q	integer
real_poly	integer[]
simple_distinct	text[]
simple_factors	text[]
simple_multiplicities	smallint[]
singular_primes	text[]
size	integer
slopes	text[]
splitting_field	text
splitting_polynomials	numeric[]
twist_count	integer
twists	jsonb
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[]

av_fq_isog • Show schema

{'abvar_count': 1408, 'abvar_counts': [1408, 3469312, 6307210624, 11676705030144, 21613209662501248, 39961436388323946496, 73885633024204801165696, 136614024425400609669120000, 252599352220579583703204662656, 467056177502959843067873422077952], 'abvar_counts_str': '1408 3469312 6307210624 11676705030144 21613209662501248 39961436388323946496 73885633024204801165696 136614024425400609669120000 252599352220579583703204662656 467056177502959843067873422077952 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.132197172840034, 0.5], 'center_dim': 4, 'cohen_macaulay_max': 3, 'curve_count': 32, 'curve_counts': [32, 1878, 79328, 3415438, 147020192, 6321648678, 271819625312, 11688200166046, 502592649038624, 21611482763302518], 'curve_counts_str': '32 1878 79328 3415438 147020192 6321648678 271819625312 11688200166046 502592649038624 21611482763302518 ', 'curves': ['y^2=22*x^6+24*x^5+5*x^4+4*x^3+5*x^2+26*x+22', 'y^2=31*x^6+6*x^5+33*x^4+28*x^3+16*x^2+19*x+42', 'y^2=x^6+23*x^5+41*x^4+23*x^3+12*x^2+6*x+28', 'y^2=16*x^6+16*x^5+12*x^4+5*x^3+30*x^2+33*x+35', 'y^2=40*x^6+13*x^5+35*x^4+20*x^3+15*x^2+35*x+23', 'y^2=41*x^6+37*x^5+37*x^4+x^3+40*x^2+11*x+23', 'y^2=17*x^6+28*x^5+41*x^4+21*x^3+41*x^2+28*x+17', 'y^2=12*x^6+38*x^5+13*x^4+23*x^3+13*x^2+38*x+12', 'y^2=23*x^6+33*x^5+20*x^4+33*x^3+11*x^2+18*x+17', 'y^2=17*x^6+36*x^5+29*x^4+20*x^3+33*x^2+13*x+3', 'y^2=5*x^6+16*x^5+9*x^4+7*x^3+40*x^2+7*x+9', 'y^2=5*x^6+14*x^5+28*x^4+21*x^3+29*x^2+6*x+33', 'y^2=16*x^6+30*x^5+41*x^4+36*x^3+26*x^2+32*x+29', 'y^2=42*x^6+35*x^5+8*x^4+37*x^3+25*x^2+3*x+24', 'y^2=42*x^6+5*x^5+6*x^4+12*x^3+5*x^2+3*x+25', 'y^2=17*x^6+41*x^5+24*x^4+21*x^3+37*x^2+24*x+36', 'y^2=17*x^6+5*x^5+15*x^4+35*x^3+34*x^2+42*x+27', 'y^2=31*x^5+35*x^4+41*x^3+35*x^2+28*x+14', 'y^2=9*x^6+17*x^5+40*x^4+x^3+23*x^2+14*x+21', 'y^2=10*x^6+17*x^5+4*x^4+10*x^3+25*x^2+28*x', 'y^2=15*x^6+3*x^5+14*x^4+8*x^3+29*x^2+x+16', 'y^2=15*x^6+28*x^5+23*x^4+27*x^3+16*x^2+35*x+3', 'y^2=29*x^6+6*x^5+23*x^4+23*x^3+12*x^2+10*x+32', 'y^2=12*x^6+15*x^5+39*x^4+10*x^3+19*x^2+24*x+12', 'y^2=27*x^6+31*x^5+16*x^4+36*x^3+16*x^2+31*x+27', 'y^2=39*x^6+24*x^5+22*x^4+40*x^3+33*x^2+28*x+26', 'y^2=12*x^6+37*x^5+15*x^4+10*x^3+4*x^2+37*x+22', 'y^2=11*x^6+14*x^5+27*x^4+28*x^3+29*x^2+20*x+26', 'y^2=41*x^6+14*x^5+39*x^4+x^3+28*x^2+7*x+18', 'y^2=23*x^6+18*x^5+31*x^4+36*x^3+2*x^2+34*x+18', 'y^2=22*x^6+21*x^5+11*x^4+24*x^3+31*x^2+6*x+26', 'y^2=8*x^6+19*x^5+38*x^4+29*x^3+x^2+13*x+6', 'y^2=26*x^6+22*x^5+30*x^4+10*x^3+13*x^2+18*x+36', 'y^2=33*x^6+29*x^5+31*x^4+35*x^3+10*x^2+15*x+34', 'y^2=7*x^6+13*x^5+9*x^4+6*x^3+39*x^2+18*x+13', 'y^2=18*x^6+21*x^5+8*x^4+37*x^3+14*x^2+26*x+14', 'y^2=37*x^6+5*x^5+27*x^4+9*x^3+7*x^2+18*x+5', 'y^2=40*x^6+25*x^5+2*x^4+18*x^3+22*x^2+9*x+35', 'y^2=35*x^6+31*x^5+29*x^4+26*x^3+41*x^2+14*x+39', 'y^2=20*x^6+16*x^5+28*x^4+41*x^3+22*x^2+40*x+38', 'y^2=42*x^6+5*x^5+28*x^4+31*x^3+40*x^2+35*x+30', 'y^2=2*x^6+22*x^5+36*x^4+23*x^3+40*x^2+x+15', 'y^2=7*x^6+11*x^5+8*x^4+33*x^3+26*x^2+31*x+18', 'y^2=26*x^6+8*x^5+25*x^4+42*x^3+30*x^2+19*x+27', 'y^2=12*x^5+29*x^4+21*x^3+33*x^2+7*x', 'y^2=5*x^6+32*x^5+31*x^4+9*x^3+31*x^2+32*x+5', 'y^2=33*x^6+24*x^5+21*x^4+29*x^3+30*x^2+25*x+26', 'y^2=36*x^6+5*x^5+9*x^4+32*x^3+39*x^2+4*x+37', 'y^2=2*x^6+30*x^5+37*x^4+23*x^3+27*x^2+40*x+3', 'y^2=20*x^6+40*x^5+37*x^4+9*x^3+18*x^2+13*x+34', 'y^2=19*x^6+19*x^5+23*x^4+34*x^3+6*x^2+3*x+12', 'y^2=26*x^6+9*x^5+34*x^4+28*x^3+34*x^2+9*x+26', 'y^2=33*x^6+20*x^5+20*x^4+2*x^3+22*x^2+5*x+27', 'y^2=39*x^6+21*x^5+38*x^4+18*x^3+5*x^2+27*x+13', 'y^2=9*x^6+16*x^5+36*x^4+32*x^3+37*x^2+x+41', 'y^2=2*x^6+26*x^5+37*x^4+16*x^3+x^2+31*x+42', 'y^2=29*x^6+29*x^5+13*x^4+4*x^3+23*x^2+14*x+28', 'y^2=39*x^6+2*x^5+29*x^4+31*x^3+19*x^2+29*x+13', 'y^2=11*x^6+11*x^5+40*x^4+32*x^3+8*x^2+41*x+28', 'y^2=40*x^6+27*x^5+19*x^4+24*x^3+36*x^2+28*x+10', 'y^2=25*x^6+5*x^5+40*x^4+11*x^3+37*x^2+35*x+42', 'y^2=23*x^6+21*x^5+3*x^4+37*x^3+x^2+31*x+25', 'y^2=22*x^6+2*x^5+40*x^4+37*x^3+16*x^2+33*x+42', 'y^2=14*x^6+18*x^5+26*x^4+17*x^3+26*x^2+18*x+14', 'y^2=34*x^6+37*x^5+28*x^4+40*x^3+12*x^2+34*x+28', 'y^2=22*x^6+7*x^5+27*x^4+9*x^3+27*x^2+7*x+22', 'y^2=29*x^6+5*x^5+x^4+25*x^3+31*x^2+38*x+12', 'y^2=32*x^6+24*x^5+15*x^4+20*x^3+2*x^2+22*x+13', 'y^2=37*x^6+38*x^5+33*x^4+36*x^3+24*x^2+25*x+2', 'y^2=8*x^6+8*x^5+38*x^4+26*x^3+41*x^2+12*x+22', 'y^2=7*x^6+19*x^5+6*x^4+13*x^3+x^2+10*x+22', 'y^2=31*x^6+28*x^5+36*x^4+40*x^3+35*x^2+x+25', 'y^2=14*x^6+41*x^5+4*x^4+6*x^3+18*x^2+6*x+16', 'y^2=28*x^6+15*x^5+35*x^4+42*x^3+37*x^2+x+25', 'y^2=21*x^6+28*x^5+16*x^4+35*x^3+20*x^2+34*x+22', 'y^2=33*x^6+20*x^5+29*x^4+5*x^3+21*x^2+15*x+21', 'y^2=42*x^6+7*x^5+9*x^4+42*x^3+31*x^2+33*x', 'y^2=37*x^6+16*x^5+30*x^4+35*x^3+32*x^2+13*x+29', 'y^2=7*x^6+29*x^5+7*x^4+41*x^3+29*x^2+10*x+21', 'y^2=15*x^6+x^5+42*x^4+20*x^2+39*x+10', 'y^2=30*x^6+2*x^5+9*x^4+19*x^3+35*x^2+33*x+21', 'y^2=20*x^6+22*x^5+10*x^4+8*x^3+42*x^2+33*x+37'], 'dim1_distinct': 2, 'dim1_factors': 2, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 28, 'g': 2, 'galois_groups': ['2T1', '2T1'], 'geom_dim1_distinct': 2, 'geom_dim1_factors': 2, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 0, 'geom_dim3_factors': 0, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 3, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['1T1', '2T1'], 'geometric_number_fields': ['1.1.1.1', '2.0.7.1'], 'geometric_splitting_field': '2.0.7.1', 'geometric_splitting_polynomials': [[2, -1, 1]], 'group_structure_count': 7, 'has_geom_ss_factor': True, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 82, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 82, 'label': '2.43.am_di', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 2, 'newton_coelevation': 1, 'newton_elevation': 1, 'noncyclic_primes': [2], 'number_fields': ['2.0.7.1', '2.0.43.1'], 'p': 43, 'p_rank': 1, 'p_rank_deficit': 1, 'poly': [1, -12, 86, -516, 1849], 'poly_str': '1 -12 86 -516 1849 ', 'primitive_models': [], 'q': 43, 'real_poly': [1, -12], 'simple_distinct': ['1.43.am', '1.43.a'], 'simple_factors': ['1.43.amA', '1.43.aA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,-F+15', '3,F^2+5*F-V+40'], 'slopes': ['0A', '1/2A', '1/2B', '1A'], 'splitting_field': '4.0.90601.2', 'splitting_polynomials': [[81, 0, 25, 0, 1]], 'twist_count': 2, 'twists': [['2.43.m_di', '2.1849.bc_abxq', 2]], 'weak_equivalence_count': 48, 'zfv_index': 576, 'zfv_index_factorization': [[2, 6], [3, 2]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 4816, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,-F+15', '3,F^2+5*F-V+40']}

Column	Type
base_label	text
extension_degree	smallint
extension_label	text
multiplicity	smallint

av_fq_endalg_factors • Show schema

id: 33560
{'base_label': '2.43.am_di', 'extension_degree': 1, 'extension_label': '1.43.am', 'multiplicity': 1}
id: 33561
{'base_label': '2.43.am_di', 'extension_degree': 1, 'extension_label': '1.43.a', 'multiplicity': 1}
id: 33562
{'base_label': '2.43.am_di', 'extension_degree': 2, 'extension_label': '1.1849.acg', 'multiplicity': 1}
id: 33563
{'base_label': '2.43.am_di', 'extension_degree': 2, 'extension_label': '1.1849.di', 'multiplicity': 1}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0', '0'], 'center': '2.0.7.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.43.am', 'galois_group': '2T1', 'places': [['18', '1'], ['24', '1']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0'], 'center': '2.0.43.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.43.a', 'galois_group': '2T1', 'places': [['21', '1']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0', '0'], 'center': '2.0.7.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.1849.acg', 'galois_group': '2T1', 'places': [['18', '1'], ['24', '1']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.1849.di', 'galois_group': '1T1', 'places': [['0']]}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.