Table av_fq_isog
Isogeny classes of abelian varieties over finite fields
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| Column |
Type |
Example |
| abvar_count |
numeric |
5034 |
| abvar_counts |
numeric[] |
[5034, 17488116, 68295940722, 281473605403776, 1153002695580424074, 4722342662695980436884, 19342808... |
| abvar_counts_str |
text |
'5034 17488116 68295940722 281473605403776 1153002695580424074 4722342662695980436884 19342808658485... |
| all_polarized_product |
boolean |
|
| all_unpolarized_product |
boolean |
|
| angle_corank |
smallint |
0 |
| angle_rank |
smallint |
2 |
| angles |
double precision[] |
[0.567229377711413, 0.681711733276293] |
| center_dim |
smallint |
4 |
| cohen_macaulay_max |
smallint |
1 |
| curve_count |
integer |
77 |
| curve_counts |
numeric[] |
[77, 4267, 260525, 16777135, 1073817437, 68719130107, 4398045498077, 281474985553759, 18014398518915... |
| curve_counts_str |
text |
'77 4267 260525 16777135 1073817437 68719130107 4398045498077 281474985553759 18014398518915245 1152... |
| curves |
text[] |
['y^2+(x^2+x+a^5+a^4+a^3+1)*y=(a^5+a^4+a^3+a^2+a)*x^5+(a^4+a^3+1)*x^3+(a^4+a^3+a^2+1)*x+a^3+a', 'y^2... |
| 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 |
2 |
| 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[] |
['4.0.3864336.3'] |
| geometric_splitting_field |
text |
'4.0.3864336.3' |
| geometric_splitting_polynomials |
numeric[] |
[[1341, 102, 102, -2, 1]] |
| group_structure_count |
smallint |
1 |
| has_geom_ss_factor |
boolean |
False |
| has_jacobian |
smallint |
1 |
| has_principal_polarization |
smallint |
1 |
| hyp_count |
integer |
216 |
| 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 |
216 |
| label |
text |
'2.64.m_gb' |
| 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[] |
[] |
| number_fields |
text[] |
['4.0.3864336.3'] |
| p |
smallint |
2 |
| p_rank |
smallint |
2 |
| p_rank_deficit |
smallint |
0 |
| pic_prime_gens |
integer[] |
|
| poly |
integer[] |
[1, 12, 157, 768, 4096] |
| poly_str |
text |
'1 12 157 768 4096 ' |
| primitive_models |
text[] |
[] |
| principal_polarization_count |
integer |
|
| q |
integer |
64 |
| real_poly |
integer[] |
[1, 12, 29] |
| simple_distinct |
text[] |
['2.64.m_gb'] |
| simple_factors |
text[] |
['2.64.m_gbA'] |
| simple_multiplicities |
smallint[] |
[1] |
| singular_primes |
text[] |
['3,-2*F^2+F'] |
| size |
integer |
|
| slopes |
text[] |
['0A', '0B', '1A', '1B'] |
| splitting_field |
text |
'4.0.3864336.3' |
| splitting_polynomials |
numeric[] |
[[1341, 102, 102, -2, 1]] |
| twist_count |
integer |
2 |
| twists |
jsonb |
[['2.64.am_gb', '2.4096.go_vif', 2]] |
| weak_equivalence_count |
smallint |
2 |
| zfv_index |
numeric |
3 |
| zfv_index_factorization |
numeric[] |
[[3, 1]] |
| zfv_is_bass |
boolean |
True |
| zfv_is_maximal |
boolean |
False |
| zfv_pic_size |
integer |
|
| zfv_plus_index |
numeric |
1 |
| zfv_plus_index_factorization |
numeric[] |
[] |
| zfv_plus_norm |
numeric |
44361 |
| zfv_singular_count |
smallint |
2 |
| zfv_singular_primes |
text[] |
['3,-2*F^2+F'] |
{'abvar_count': 11, 'abvar_counts': [11, 143, 1364, 14443, 160501, 1773200, 19494871, 214348563, 2357852684, 25937443103], 'abvar_counts_str': '11 143 1364 14443 160501 1773200 19494871 214348563 2357852684 25937443103 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 1, 'angles': [0.45182932554789], 'center_dim': 2, 'cohen_macaulay_max': 1, 'curve_count': 11, 'curve_counts': [11, 143, 1364, 14443, 160501, 1773200, 19494871, 214348563, 2357852684, 25937443103], 'curve_counts_str': '11 143 1364 14443 160501 1773200 19494871 214348563 2357852684 25937443103 ', 'curves': ['y^2=x^3+4*x+4'], 'dim1_distinct': 1, 'dim1_factors': 1, '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': 1, 'g': 1, 'galois_groups': ['2T1'], 'geom_dim1_distinct': 1, 'geom_dim1_factors': 1, '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': 2, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.43.1'], 'geometric_splitting_field': '2.0.43.1', 'geometric_splitting_polynomials': [[11, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 0, 'id': 68, 'is_cyclic': True, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 1, 'label': '1.11.ab', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 1, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['2.0.43.1'], 'p': 11, 'p_rank': 1, 'p_rank_deficit': 0, 'pic_prime_gens': [], 'poly': [1, -1, 11], 'poly_str': '1 -1 11 ', 'primitive_models': [], 'principal_polarization_count': 1, 'q': 11, 'real_poly': [1, -1], 'simple_distinct': ['1.11.ab'], 'simple_factors': ['1.11.abA'], 'simple_multiplicities': [1], 'singular_primes': [], 'size': 1, 'slopes': ['0A', '1A'], 'splitting_field': '2.0.43.1', 'splitting_polynomials': [[11, -1, 1]], 'twist_count': 2, 'twists': [['1.11.b', '1.121.v', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_pic_size': 1, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 43, 'zfv_singular_count': 0, 'zfv_singular_primes': []}