Database - av_fq_isog

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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	14759
abvar_counts	numeric[]	[14759, 231908167, 3913915019999, 59389102981791127, 931867946174304461639, 145522874045272391862079...
abvar_counts_str	text	'14759 231908167 3913915019999 59389102981791127 931867946174304461639 14552287404527239186207951 22...
all_polarized_product	boolean
all_unpolarized_product	boolean
angle_corank	smallint	0
angle_rank	smallint	3
angles	double precision[]	[0.163478502011679, 0.426593345341528, 0.990610460402604]
center_dim	smallint	6
cohen_macaulay_max	smallint
curve_count	integer	25
curve_counts	numeric[]	[25, 595, 16027, 389211, 9771345, 244146871, 6103965116, 152587786035, 3814697967505, 95367391825255...
curve_counts_str	text	'25 595 16027 389211 9771345 244146871 6103965116 152587786035 3814697967505 95367391825255 '
curves	text[]	['y^2=x^7+x^5+(2*a+1)*x^4+(a+1)*x^3+(3*a+2)*x^2+2*a*x+4*a+2', 'y^2=a*x^7+2*a*x^5+(3*a+4)*x^3+2*a*x^2...
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[]	['6.0.944035591833799.1']
geometric_splitting_field	text	'6.0.944035591833799.1'
geometric_splitting_polynomials	numeric[]	[[15625, -625, -375, 149, -15, -1, 1]]
group_structure_count	smallint
has_geom_ss_factor	boolean	False
has_jacobian	smallint	1
has_principal_polarization	smallint	1
hyp_count	integer	3
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	'3.25.ab_ap_ft'
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[]	['6.0.944035591833799.1']
p	smallint	5
p_rank	smallint	3
p_rank_deficit	smallint	0
pic_prime_gens	integer[]
poly	integer[]	[1, -1, -15, 149, -375, -625, 15625]
poly_str	text	'1 -1 -15 149 -375 -625 15625 '
primitive_models	text[]	[]
principal_polarization_count	integer
q	integer	25
real_poly	integer[]	[1, -1, -90, 199]
simple_distinct	text[]	['3.25.ab_ap_ft']
simple_factors	text[]	['3.25.ab_ap_ftA']
simple_multiplicities	smallint[]	[1]
singular_primes	text[]
size	integer	498
slopes	text[]	['0A', '0B', '0C', '1A', '1B', '1C']
splitting_field	text	'6.0.944035591833799.1'
splitting_polynomials	numeric[]	[[15625, -625, -375, 149, -15, -1, 1]]
twist_count	integer	2
twists	jsonb	[['3.25.b_ap_aft', '3.625.abf_ait_bcer', 2]]
weak_equivalence_count	smallint
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	199
zfv_singular_count	smallint
zfv_singular_primes	text[]

{'abvar_count': 1868, 'abvar_counts': [1868, 3489424, 6321269036, 11711288574976, 21611482568949068, 39958442225492369296, 73885357343597305826732, 136613919453834080760643584, 252599333573499012746530597964, 467056178827989407700593978068624], 'abvar_counts_str': '1868 3489424 6321269036 11711288574976 21611482568949068 39958442225492369296 73885357343597305826732 136613919453834080760643584 252599333573499012746530597964 467056178827989407700593978068624 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.28355963856863, 0.71644036143137], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 44, 'curve_counts': [44, 1886, 79508, 3425550, 147008444, 6321175022, 271818611108, 11688191185054, 502592611936844, 21611482824613886], 'curve_counts_str': '44 1886 79508 3425550 147008444 6321175022 271818611108 11688191185054 502592611936844 21611482824613886 ', 'curves': ['y^2=3*x^6+24*x^5+38*x^4+24*x^3+13*x^2+29*x', 'y^2=9*x^6+29*x^5+28*x^4+29*x^3+39*x^2+x', 'y^2=10*x^6+26*x^5+34*x^4+31*x^3+11*x^2+24*x+14', 'y^2=30*x^6+35*x^5+16*x^4+7*x^3+33*x^2+29*x+42', 'y^2=11*x^6+3*x^5+31*x^4+29*x^3+21*x^2+4*x+27', 'y^2=33*x^6+9*x^5+7*x^4+x^3+20*x^2+12*x+38', 'y^2=32*x^6+7*x^5+32*x^4+16*x^3+19*x^2+30*x+24', 'y^2=10*x^6+21*x^5+10*x^4+5*x^3+14*x^2+4*x+29', 'y^2=36*x^6+11*x^5+25*x^4+29*x^3+3*x^2+39', 'y^2=22*x^6+33*x^5+32*x^4+x^3+9*x^2+31', 'y^2=32*x^6+15*x^5+41*x^4+39*x^3+12*x+20', 'y^2=10*x^6+2*x^5+37*x^4+31*x^3+36*x+17', 'y^2=41*x^6+5*x^5+26*x^4+14*x^3+25*x^2+24*x+41', 'y^2=37*x^6+15*x^5+35*x^4+42*x^3+32*x^2+29*x+37', 'y^2=x^6+3*x^5+35*x^4+42*x^3+15*x^2+30*x+33', 'y^2=3*x^6+9*x^5+19*x^4+40*x^3+2*x^2+4*x+13', 'y^2=4*x^6+8*x^5+12*x^4+37*x^3+21*x^2+3*x+8', 'y^2=5*x^6+31*x^5+8*x^4+3*x^3+33*x^2+29*x+15', 'y^2=15*x^6+7*x^5+24*x^4+9*x^3+13*x^2+x+2', 'y^2=20*x^6+28*x^5+15*x^4+27*x^3+26*x^2+24*x+32', 'y^2=17*x^6+41*x^5+2*x^4+38*x^3+35*x^2+29*x+10', 'y^2=42*x^6+42*x^5+28*x^4+2*x^3+10*x^2+x+7', 'y^2=40*x^6+40*x^5+41*x^4+6*x^3+30*x^2+3*x+21', 'y^2=14*x^6+23*x^5+36*x^4+x^3+35*x^2+32*x+31', 'y^2=42*x^6+26*x^5+22*x^4+3*x^3+19*x^2+10*x+7', 'y^2=4*x^6+19*x^5+30*x^4+35*x^3+13*x^2+16*x+11', 'y^2=12*x^6+14*x^5+4*x^4+19*x^3+39*x^2+5*x+33', 'y^2=5*x^6+6*x^5+20*x^4+29*x^3+42*x^2+26*x+42', 'y^2=15*x^6+18*x^5+17*x^4+x^3+40*x^2+35*x+40', 'y^2=26*x^6+30*x^5+14*x^4+3*x^3+3*x^2+27', 'y^2=35*x^6+4*x^5+42*x^4+9*x^3+9*x^2+38', 'y^2=17*x^6+28*x^5+16*x^4+18*x^3+15*x^2+17*x+2', 'y^2=8*x^6+41*x^5+5*x^4+11*x^3+2*x^2+8*x+6', 'y^2=5*x^6+35*x^5+18*x^4+21*x^3+x^2+14*x+22', 'y^2=15*x^6+19*x^5+11*x^4+20*x^3+3*x^2+42*x+23', 'y^2=2*x^6+12*x^5+37*x^4+23*x^3+11*x^2+26*x+4', 'y^2=26*x^6+19*x^5+32*x^4+5*x^3+14*x^2+x+24', 'y^2=35*x^6+14*x^5+10*x^4+15*x^3+42*x^2+3*x+29', 'y^2=20*x^6+34*x^5+26*x^4+23*x^3+31*x^2+22*x+38', 'y^2=6*x^6+27*x^5+26*x^4+30*x^3+15*x^2+18*x+35', 'y^2=18*x^6+38*x^5+35*x^4+4*x^3+2*x^2+11*x+19', 'y^2=37*x^6+2*x^5+21*x^4+5*x^3+32*x^2+27*x+11', 'y^2=25*x^6+6*x^5+20*x^4+15*x^3+10*x^2+38*x+33', 'y^2=14*x^6+11*x^5+36*x^4+21*x^3+25*x^2+41*x+13', 'y^2=42*x^6+33*x^5+22*x^4+20*x^3+32*x^2+37*x+39', 'y^2=24*x^6+36*x^5+17*x^4+10*x^3+10*x^2+12*x+3', 'y^2=29*x^6+22*x^5+8*x^4+30*x^3+30*x^2+36*x+9', 'y^2=12*x^6+24*x^5+18*x^4+9*x^3+28*x^2+20*x+39', 'y^2=36*x^6+29*x^5+11*x^4+27*x^3+41*x^2+17*x+31', 'y^2=24*x^6+13*x^5+18*x^3+17*x^2+21*x+40', 'y^2=29*x^6+39*x^5+11*x^3+8*x^2+20*x+34', 'y^2=9*x^6+30*x^5+13*x^4+14*x^3+20*x^2+40*x+8', 'y^2=27*x^6+4*x^5+39*x^4+42*x^3+17*x^2+34*x+24', 'y^2=29*x^6+9*x^5+8*x^4+38*x^3+9*x^2+24*x+19', 'y^2=x^6+27*x^5+24*x^4+28*x^3+27*x^2+29*x+14', 'y^2=14*x^6+14*x^5+12*x^4+30*x^3+15*x^2+13*x+29', 'y^2=42*x^6+42*x^5+36*x^4+4*x^3+2*x^2+39*x+1', 'y^2=11*x^6+32*x^5+10*x^4+6*x^3+18*x^2+28*x+27', 'y^2=23*x^6+38*x^5+14*x^4+31*x^3+32*x^2+16*x+5', 'y^2=23*x^6+41*x^5+2*x^4+11*x^3+40*x^2+36*x+1', 'y^2=26*x^6+37*x^5+6*x^4+33*x^3+34*x^2+22*x+3', 'y^2=33*x^6+32*x^5+35*x^4+28*x^3+7*x^2+7*x+24', 'y^2=13*x^6+10*x^5+19*x^4+41*x^3+21*x^2+21*x+29', 'y^2=17*x^6+33*x^5+13*x^4+32*x^3+28*x^2+19*x+29', 'y^2=36*x^6+22*x^5+36*x^4+24*x^3+16*x^2+4*x+33', 'y^2=22*x^6+23*x^5+22*x^4+29*x^3+5*x^2+12*x+13', 'y^2=42*x^6+11*x^5+38*x^4+6*x^3+9*x^2+42*x+22', 'y^2=40*x^6+33*x^5+28*x^4+18*x^3+27*x^2+40*x+23', 'y^2=23*x^6+41*x^5+25*x^4+37*x^3+18*x^2+41*x+1', 'y^2=26*x^6+37*x^5+32*x^4+25*x^3+11*x^2+37*x+3', 'y^2=6*x^6+28*x^5+2*x^4+12*x^3+24*x^2+23*x+37', 'y^2=18*x^6+41*x^5+6*x^4+36*x^3+29*x^2+26*x+25', 'y^2=39*x^6+34*x^5+35*x^4+28*x^3+32*x^2+33*x+20', 'y^2=31*x^6+16*x^5+19*x^4+41*x^3+10*x^2+13*x+17', 'y^2=10*x^6+39*x^5+22*x^4+12*x^3+19*x^2+32*x+3', 'y^2=30*x^6+31*x^5+23*x^4+36*x^3+14*x^2+10*x+9', 'y^2=29*x^6+41*x^5+9*x^4+4*x^3+24*x^2+12*x+4', 'y^2=x^6+37*x^5+27*x^4+12*x^3+29*x^2+36*x+12', 'y^2=x^6+24*x^5+40*x^4+32*x^3+22*x^2+31*x+21', 'y^2=3*x^6+29*x^5+34*x^4+10*x^3+23*x^2+7*x+20', 'y^2=4*x^6+6*x^5+24*x^4+34*x^3+34*x^2+21*x+27', 'y^2=11*x^6+29*x^5+2*x^4+26*x^3+6*x^2+3*x+39', 'y^2=5*x^6+15*x^5+10*x^4+7*x^3+40*x^2+41*x+29', 'y^2=15*x^6+2*x^5+30*x^4+21*x^3+34*x^2+37*x+1', 'y^2=9*x^6+35*x^5+14*x^4+9*x^3+30*x^2+32*x+4', 'y^2=27*x^6+19*x^5+42*x^4+27*x^3+4*x^2+10*x+12', 'y^2=x^6+24*x^5+37*x^4+26*x^3+4*x^2+25*x+17', 'y^2=3*x^6+29*x^5+25*x^4+35*x^3+12*x^2+32*x+8', 'y^2=8*x^6+22*x^5+39*x^4+28*x^3+38*x^2+29*x+21', 'y^2=34*x^6+39*x^5+2*x^4+24*x^3+36*x^2+39*x', 'y^2=16*x^6+31*x^5+6*x^4+29*x^3+22*x^2+31*x', 'y^2=26*x^6+26*x^5+5*x^4+15*x^3+11*x^2+17*x+17', 'y^2=35*x^6+35*x^5+15*x^4+2*x^3+33*x^2+8*x+8', 'y^2=37*x^6+24*x^5+3*x^4+7*x^3+39*x^2+14*x+1', 'y^2=25*x^6+29*x^5+9*x^4+21*x^3+31*x^2+42*x+3', 'y^2=14*x^5+24*x^4+24*x^3+19*x^2+14*x', 'y^2=35*x^6+22*x^5+32*x^4+28*x^3+31*x^2+24*x+25', 'y^2=19*x^6+23*x^5+10*x^4+41*x^3+7*x^2+29*x+32', 'y^2=30*x^6+30*x^5+9*x^4+3*x^3+3*x^2+14*x+1', 'y^2=4*x^6+4*x^5+27*x^4+9*x^3+9*x^2+42*x+3', 'y^2=22*x^6+27*x^5+8*x^4+12*x^3+31*x^2+37*x+34', 'y^2=23*x^6+38*x^5+24*x^4+36*x^3+7*x^2+25*x+16', 'y^2=41*x^6+4*x^5+4*x^4+40*x^3+20*x^2+14*x+8', 'y^2=8*x^6+27*x^5+3*x^4+2*x^3+25*x^2+26*x+35', 'y^2=29*x^6+36*x^4+15*x^3+13*x^2+15*x+2', 'y^2=x^6+22*x^4+2*x^3+39*x^2+2*x+6', 'y^2=14*x^6+21*x^5+12*x^4+17*x^3+19*x^2+31*x+18', 'y^2=42*x^6+20*x^5+36*x^4+8*x^3+14*x^2+7*x+11', 'y^2=33*x^6+35*x^5+29*x^4+x^3+12*x^2+13*x+26', 'y^2=13*x^6+19*x^5+x^4+3*x^3+36*x^2+39*x+35', 'y^2=40*x^6+31*x^5+x^4+30*x^3+6*x^2+7*x+39', 'y^2=34*x^6+7*x^5+3*x^4+4*x^3+18*x^2+21*x+31', 'y^2=42*x^6+10*x^5+22*x^4+23*x^3+33*x^2+19*x+7', 'y^2=40*x^6+30*x^5+23*x^4+26*x^3+13*x^2+14*x+21', 'y^2=26*x^6+38*x^5+29*x^4+8*x^3+21*x^2+21*x+9', 'y^2=22*x^6+9*x^5+x^4+14*x^3+5*x^2+31*x+38', 'y^2=23*x^6+27*x^5+3*x^4+42*x^3+15*x^2+7*x+28', 'y^2=22*x^6+22*x^5+33*x^4+20*x^3+42*x^2+18*x+17', 'y^2=23*x^6+23*x^5+13*x^4+17*x^3+40*x^2+11*x+8', 'y^2=19*x^6+27*x^5+26*x^4+13*x^3+29*x^2+37*x+3', 'y^2=14*x^6+38*x^5+35*x^4+39*x^3+x^2+25*x+9', 'y^2=12*x^6+26*x^5+2*x^4+28*x^3+35*x^2+42*x+15', 'y^2=36*x^6+35*x^5+6*x^4+41*x^3+19*x^2+40*x+2', 'y^2=9*x^6+13*x^5+39*x^4+42*x^3+29*x^2+38*x+40', 'y^2=27*x^6+39*x^5+31*x^4+40*x^3+x^2+28*x+34', 'y^2=42*x^6+33*x^5+10*x^4+35*x^3+6*x^2+36*x+41', 'y^2=40*x^6+13*x^5+30*x^4+19*x^3+18*x^2+22*x+37', 'y^2=36*x^6+25*x^5+30*x^4+x^3+32*x^2+15*x+16', 'y^2=22*x^6+32*x^5+4*x^4+3*x^3+10*x^2+2*x+5', 'y^2=36*x^6+2*x^5+3*x^4+14*x^3+36*x^2+30*x+30', 'y^2=30*x^6+3*x^5+37*x^4+34*x^3+28*x^2+31*x+39', 'y^2=4*x^6+9*x^5+25*x^4+16*x^3+41*x^2+7*x+31', 'y^2=35*x^6+20*x^5+20*x^4+4*x^3+21*x^2+10*x+23', 'y^2=19*x^6+17*x^5+17*x^4+12*x^3+20*x^2+30*x+26', 'y^2=32*x^6+20*x^5+x^4+23*x^3+41*x^2+38*x+41', 'y^2=10*x^6+17*x^5+3*x^4+26*x^3+37*x^2+28*x+37', 'y^2=40*x^6+14*x^5+24*x^4+13*x^3+22*x^2+15*x+5', 'y^2=34*x^6+42*x^5+29*x^4+39*x^3+23*x^2+2*x+15', 'y^2=28*x^6+30*x^5+3*x^3+18*x+13', 'y^2=39*x^6+20*x^5+20*x^4+11*x^3+25*x^2+42*x+11', 'y^2=29*x^6+25*x^5+4*x^4+21*x^3+21*x^2+36*x+9', 'y^2=x^6+32*x^5+12*x^4+20*x^3+20*x^2+22*x+27', 'y^2=18*x^6+20*x^5+42*x^4+30*x^3+30*x^2+7*x+40', 'y^2=11*x^6+17*x^5+40*x^4+4*x^3+4*x^2+21*x+34', 'y^2=21*x^6+37*x^5+30*x^4+6*x^3+21*x^2+18*x+5', 'y^2=20*x^6+25*x^5+4*x^4+18*x^3+20*x^2+11*x+15', 'y^2=22*x^6+16*x^5+8*x^4+34*x^3+30*x^2+8*x+25', 'y^2=23*x^6+5*x^5+24*x^4+16*x^3+4*x^2+24*x+32', 'y^2=23*x^6+37*x^4+4*x^3+7*x^2+21*x+23', 'y^2=26*x^6+25*x^4+12*x^3+21*x^2+20*x+26', 'y^2=15*x^6+20*x^5+29*x^4+26*x^3+21*x^2+16*x+19', 'y^2=2*x^6+17*x^5+x^4+35*x^3+20*x^2+5*x+14', 'y^2=37*x^6+26*x^5+11*x^4+31*x^3+42*x^2+x+39', 'y^2=25*x^6+35*x^5+33*x^4+7*x^3+40*x^2+3*x+31', 'y^2=42*x^6+24*x^5+31*x^4+7*x^3+32*x^2+13*x+18', 'y^2=40*x^6+29*x^5+7*x^4+21*x^3+10*x^2+39*x+11'], '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': 5, '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': ['2.0.1768.1'], 'geometric_splitting_field': '2.0.1768.1', 'geometric_splitting_polynomials': [[442, 0, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 156, 'id': 25209, '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': 156, 'label': '2.43.a_s', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.3125824.2'], 'p': 43, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, 0, 18, 0, 1849], 'poly_str': '1 0 18 0 1849 ', 'primitive_models': [], 'q': 43, 'real_poly': [1, 0, -68], 'simple_distinct': ['2.43.a_s'], 'simple_factors': ['2.43.a_sA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-F-3'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.3125824.2', 'splitting_polynomials': [[926, -44, 45, -2, 1]], 'twist_count': 2, 'twists': [['2.43.a_as', '2.3418801.jzo_bnwswc', 4]], 'weak_equivalence_count': 5, 'zfv_index': 16, 'zfv_index_factorization': [[2, 4]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 4, 'zfv_plus_index_factorization': [[2, 2]], 'zfv_plus_norm': 10816, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-F-3']}