Database - ec_curvedata

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Query: /api/ec_curvedata/?degree=5&_offset=0

Table ec_curvedata

Elliptic curves over $\Q$.

Column	Type	Example
Ciso	text	'342475b'
Clabel	text	'342475b1'
Cnumber	smallint	1
abc_quality	double precision	0.8400271910853558
absD	numeric	3119890741625
adelic_genus	integer	0
adelic_index	integer	2
adelic_level	bigint	2660
ainvs	numeric[]	[1, 1, 1, 1527, 82456]
analytic_rank	smallint	1
bad_primes	integer[]	[5, 7, 19, 103]
class_deg	smallint	1
class_size	smallint	1
cm	smallint	0
conductor	integer	342475
degree	bigint	321408
elladic_images	text[]	[]
faltings_height	numeric	1.0788524859857993964376520983
faltings_index	smallint	0
faltings_ratio	smallint	1
intrinsic_torsion	smallint	1
iso_nlabel	smallint	1
isogeny_degrees	smallint[]	[1]
jinv	numeric[]	[3150017993179, 24959125933]
lmfdb_iso	text	'342475.b'
lmfdb_label	text	'342475.b1'
lmfdb_number	smallint	1
manin_constant	smallint	1
min_quad_twist_ainvs	numeric[]	[1, 1, 1, 1527, 82456]
min_quad_twist_disc	smallint	1
modell_images	text[]	[]
modm_images	text[]	['2660.2.0.?']
nonmax_primes	smallint[]	[]
nonmax_rad	integer	1
num_bad_primes	smallint	4
num_int_pts	integer	4
optimality	smallint	1
potential_good_reduction	boolean	False
rank	smallint	1
regulator	numeric	1.0994680030176458464063835871
semistable	boolean	False
serre_invariants	integer[]	[[2, 2, 665], [3, 2, 2575], [5, 10, 13699], [7, 8, 48925], [19, 20, 18025], [103, 104, 3325]]
sha	integer	1
sha_primes	smallint[]	[]
signD	smallint	-1
squarefree_disc	boolean
stable_faltings_height	numeric	0.67649300787727430278746226499
szpiro_ratio	double precision	2.8364586164532186
torsion	smallint	1
torsion_primes	smallint[]	[]
torsion_structure	smallint[]	[]

0. lmfdb_label: 11.a1
   {'Ciso': '11a', 'Clabel': '11a2', 'Cnumber': 2, 'abc_quality': 1.0929566831983986, 'absD': 11, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 550, 'ainvs': [0, -1, 1, -7820, -263580], 'analytic_rank': 0, 'bad_primes': [11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 11, 'degree': 5, 'elladic_images': ['25.120.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540515', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 25, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '11.a', 'lmfdb_label': '11.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '22.2.0.a.1', '25.120.0-25.a.2.2', '110.48.1.?', '275.600.12.?', '550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[11, 12, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540515', 'prec': 97}, 'szpiro_ratio': 16.058687318281603, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
1. lmfdb_label: 11.a3
   {'Ciso': '11a', 'Clabel': '11a3', 'Cnumber': 3, 'abc_quality': 0.8254556483942886, 'absD': 11, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 550, 'ainvs': [0, -1, 1, 0, 0], 'analytic_rank': 0, 'bad_primes': [11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 11, 'degree': 5, 'elladic_images': ['25.120.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 5, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-4096, 11], 'lmfdb_iso': '11.a', 'lmfdb_label': '11.a3', 'lmfdb_number': 3, 'manin_constant': 5, 'min_quad_twist_ainvs': [0, -1, 1, 0, 0], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.1'], 'modm_images': ['5.24.0-5.a.1.2', '22.2.0.a.1', '25.120.0-25.a.1.2', '110.48.1.?', '275.600.12.?', '550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 1, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[11, 12, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 97}, 'szpiro_ratio': 4.190241815676422, 'torsion': 5, 'torsion_primes': [5], 'torsion_structure': [5]}
2. lmfdb_label: 46.a2
   {'Ciso': '46a', 'Clabel': '46a1', 'Cnumber': 1, 'abc_quality': 1.0342185338851655, 'absD': 23552, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 184, 'ainvs': [1, -1, 0, -10, -12], 'analytic_rank': 0, 'bad_primes': [2, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 46, 'degree': 5, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.43848206462462840707965101087', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-116930169, 23552], 'lmfdb_iso': '46.a', 'lmfdb_label': '46.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -10, -12], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '46.6.0.a.1', '184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 23], [5, 2, 23], [23, 24, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43848206462462840707965101087', 'prec': 97}, 'szpiro_ratio': 4.930142729087303, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
3. lmfdb_label: 67.a1
   {'Ciso': '67a', 'Clabel': '67a1', 'Cnumber': 1, 'abc_quality': 0.8765587928270674, 'absD': 67, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 134, 'ainvs': [0, 1, 1, -12, -21], 'analytic_rank': 0, 'bad_primes': [67], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 67, 'degree': 5, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.67526661334726782079910049622', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-207474688, 67], 'lmfdb_iso': '67.a', 'lmfdb_label': '67.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -12, -21], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['134.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[67, 68, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67526661334726782079910049622', 'prec': 97}, 'szpiro_ratio': 4.554691509527169, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
4. lmfdb_label: 89.b2
   {'Ciso': '89b', 'Clabel': '89b1', 'Cnumber': 1, 'abc_quality': 0.8467296169723478, 'absD': 7921, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 712, 'ainvs': [1, 1, 0, 4, 5], 'analytic_rank': 0, 'bad_primes': [89], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 89, 'degree': 5, 'elladic_images': ['8.12.0.37'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.56692298016954181123104544870', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [4657463, 7921], 'lmfdb_iso': '89.b', 'lmfdb_label': '89.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 4, 5], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '8.12.0-4.a.1.1', '356.12.0.?', '712.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [89, 90, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56692298016954181123104544870', 'prec': 97}, 'szpiro_ratio': 3.5681361497532884, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}