Table av_fq_isog
Isogeny classes of abelian varieties over finite fields
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| Column |
Type |
Example |
| abvar_count |
numeric |
3976 |
| abvar_counts |
numeric[] |
[3976, 16770768, 62854898176, 281474968675488, 1152921504800775976, 4716923723276098424832, 19342813... |
| abvar_counts_str |
text |
'3976 16770768 62854898176 281474968675488 1152921504800775976 4716923723276098424832 19342813113840... |
| all_polarized_product |
boolean |
|
| all_unpolarized_product |
boolean |
|
| angle_corank |
smallint |
2 |
| angle_rank |
smallint |
1 |
| angles |
double precision[] |
[0.035252284011892, 0.631414382654775, 0.701918950678559] |
| center_dim |
smallint |
6 |
| cohen_macaulay_max |
smallint |
1 |
| curve_count |
integer |
17 |
| curve_counts |
numeric[] |
[17, 257, 3734, 65537, 1048577, 16757870, 268435457, 4294967297, 68718622598, 1099511627777] |
| curve_counts_str |
text |
'17 257 3734 65537 1048577 16757870 268435457 4294967297 68718622598 1099511627777 ' |
| curves |
text[] |
['y^2+(a*x^4+a*x^3+a*x)*y=(a+1)*x', 'y^2+(a*x^4+a*x^3+a*x)*y=(a^2+a+1)*x', 'y^2+(a*x^4+a*x^3+a*x)*y=... |
| 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 |
1 |
| g |
smallint |
3 |
| galois_groups |
text[] |
['6T3'] |
| geom_dim1_distinct |
smallint |
1 |
| geom_dim1_factors |
smallint |
3 |
| geom_dim2_distinct |
smallint |
0 |
| geom_dim2_factors |
smallint |
0 |
| 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 |
2 |
| geometric_extension_degree |
smallint |
3 |
| geometric_galois_groups |
text[] |
['2T1'] |
| geometric_number_fields |
text[] |
['2.0.1743.1'] |
| geometric_splitting_field |
text |
'2.0.1743.1' |
| geometric_splitting_polynomials |
numeric[] |
[[436, -1, 1]] |
| group_structure_count |
smallint |
1 |
| has_geom_ss_factor |
boolean |
False |
| has_jacobian |
smallint |
1 |
| has_principal_polarization |
smallint |
1 |
| hyp_count |
integer |
20 |
| is_cyclic |
boolean |
True |
| is_geometrically_simple |
boolean |
False |
| is_geometrically_squarefree |
boolean |
False |
| is_primitive |
boolean |
True |
| is_simple |
boolean |
True |
| is_squarefree |
boolean |
True |
| is_supersingular |
boolean |
False |
| jacobian_count |
integer |
|
| label |
text |
'3.16.a_a_aer' |
| max_divalg_dim |
smallint |
1 |
| max_geom_divalg_dim |
smallint |
1 |
| max_twist_degree |
integer |
6 |
| newton_coelevation |
smallint |
4 |
| newton_elevation |
smallint |
0 |
| noncyclic_primes |
integer[] |
[] |
| number_fields |
text[] |
['6.0.3860287847703.3'] |
| p |
smallint |
2 |
| p_rank |
smallint |
3 |
| p_rank_deficit |
smallint |
0 |
| pic_prime_gens |
integer[] |
|
| poly |
integer[] |
[1, 0, 0, -121, 0, 0, 4096] |
| poly_str |
text |
'1 0 0 -121 0 0 4096 ' |
| primitive_models |
text[] |
[] |
| principal_polarization_count |
integer |
|
| q |
integer |
16 |
| real_poly |
integer[] |
[1, 0, -48, -121] |
| simple_distinct |
text[] |
['3.16.a_a_aer'] |
| simple_factors |
text[] |
['3.16.a_a_aerA'] |
| simple_multiplicities |
smallint[] |
[1] |
| singular_primes |
text[] |
[] |
| size |
integer |
|
| slopes |
text[] |
['0A', '0B', '0C', '1A', '1B', '1C'] |
| splitting_field |
text |
'6.0.6644213163.2' |
| splitting_polynomials |
numeric[] |
[[17104, -2856, 333, -196, -3, 0, 1]] |
| twist_count |
integer |
2 |
| twists |
jsonb |
[['3.16.a_a_er', '3.256.a_a_ajob', 2], ['3.16.a_a_er', '3.16777216.abcqd_otemit_aekfsjaybh', 6]] |
| weak_equivalence_count |
smallint |
1 |
| zfv_index |
numeric |
1 |
| zfv_index_factorization |
numeric[] |
[] |
| zfv_is_bass |
boolean |
True |
| zfv_is_maximal |
boolean |
True |
| zfv_pic_size |
integer |
|
| zfv_plus_index |
numeric |
1 |
| zfv_plus_index_factorization |
numeric[] |
[] |
| zfv_plus_norm |
numeric |
1743 |
| zfv_singular_count |
smallint |
0 |
| zfv_singular_primes |
text[] |
[] |
{'abvar_count': 264, 'abvar_counts': [264, 69696, 24142536, 6959563776, 2015996558664, 582862044511296, 168377826405140616, 48663388413005414400, 14063084451830590788744, 4064242124545090793464896], 'abvar_counts_str': '264 69696 24142536 6959563776 2015996558664 582862044511296 168377826405140616 48663388413005414400 14063084451830590788744 4064242124545090793464896 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.111442130273348, 0.888557869726652], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 18, 'curve_counts': [18, 238, 4914, 83326, 1419858, 24147502, 410338674, 6976072318, 118587876498, 2015999216878], 'curve_counts_str': '18 238 4914 83326 1419858 24147502 410338674 6976072318 118587876498 2015999216878 ', 'curves': ['y^2=4*x^6+10*x^5+6*x^3+x^2+x+11', 'y^2=16*x^6+16*x^5+14*x^3+3*x^2+1', 'y^2=14*x^6+9*x^4+6*x^3+10*x^2+11*x+4', 'y^2=x^6+16*x^5+13*x^4+4*x^3+7*x^2+3*x+13', 'y^2=13*x^6+2*x^5+2*x^4+3*x^3+3*x^2+9*x+10', 'y^2=11*x^6+x^5+6*x^4+8*x^2+4*x+2', 'y^2=5*x^6+6*x^5+2*x^4+3*x^3+10*x^2+14*x+13', 'y^2=14*x^6+6*x^5+2*x^4+15*x^3+11*x^2+3*x+13'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 1, 'dim2_factors': 1, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 4, 'g': 2, 'galois_groups': ['4T2'], 'geom_dim1_distinct': 1, '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': 2, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.120.1'], 'geometric_splitting_field': '2.0.120.1', 'geometric_splitting_polynomials': [[30, 0, 1]], 'group_structure_count': 3, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 8, 'id': 8888, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 8, 'label': '2.17.a_aba', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 8, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.57600.2'], 'p': 17, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, 0, -26, 0, 289], 'poly_str': '1 0 -26 0 289 ', 'primitive_models': [], 'q': 17, 'real_poly': [1, 0, -60], 'simple_distinct': ['2.17.a_aba'], 'simple_factors': ['2.17.a_abaA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-2*F+V+3'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.57600.2', 'splitting_polynomials': [[49, 0, 16, 0, 1]], 'twist_count': 4, 'twists': [['2.17.a_ba', '2.83521.aho_kbic', 4], ['2.17.ae_i', '2.6975757441.rxuq_evkkvuws', 8], ['2.17.e_i', '2.6975757441.rxuq_evkkvuws', 8]], 'weak_equivalence_count': 5, 'zfv_index': 8, 'zfv_index_factorization': [[2, 3]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 64, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-2*F+V+3']}
