LMFDB - Elliptic curve data

Formats: - HTML - YAML - JSON - 2026-04-18T14:44:26.546376

Column	Type
Ciso	text
Clabel	text
Cnumber	smallint
abc_quality	double precision
absD	numeric
adelic_genus	integer
adelic_index	integer
adelic_level	bigint
ainvs	numeric[]
analytic_rank	smallint
bad_primes	integer[]
class_deg	smallint
class_size	smallint
cm	smallint
conductor	integer
degree	bigint
elladic_images	text[]
faltings_height	numeric
faltings_index	smallint
faltings_ratio	smallint
intrinsic_torsion	smallint
iso_nlabel	smallint
isogeny_degrees	smallint[]
jinv	numeric[]
lmfdb_iso	text
lmfdb_label	text
lmfdb_number	smallint
manin_constant	smallint
min_quad_twist_ainvs	numeric[]
min_quad_twist_disc	smallint
modell_images	text[]
modm_images	text[]
nonmax_primes	smallint[]
nonmax_rad	integer
num_bad_primes	smallint
num_int_pts	integer
optimality	smallint
potential_good_reduction	boolean
rank	smallint
regulator	numeric
semistable	boolean
serre_invariants	integer[]
sha	integer
sha_primes	smallint[]
signD	smallint
squarefree_disc	boolean
stable_faltings_height	numeric
szpiro_ratio	double precision
torsion	smallint
torsion_primes	smallint[]
torsion_structure	smallint[]

ec_curvedata • Show schema

{'Ciso': '2184b', 'Clabel': '2184b2', 'Cnumber': 2, 'abc_quality': 0.8759622866765943, 'absD': 76317696, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [0, -1, 0, -112, 220], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2184, 'degree': 640, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.20597656995231632818177958883', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [153091012, 74529], 'lmfdb_iso': '2184.g', 'lmfdb_label': '2184.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -112, 220], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '52.12.0-2.a.1.1', '84.12.0.?', '104.24.0.?', '168.24.0.?', '1092.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 728], [7, 8, 312], [13, 14, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37164608051430476299924717905', 'prec': 107}, 'szpiro_ratio': 3.3526213430164087, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}

Column	Type
anlist	smallint[]
aplist	smallint[]
class_deg	smallint
class_size	smallint
conductor	integer
isogeny_matrix	smallint[]
lmfdb_iso	text
trace_hash	bigint

ec_classdata • Show schema

{'anlist': [0, 1, 0, -1, 0, 2, 0, 1, 0, 1, 0, -4, 0, -1, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, -1, 2, 1, -4, -1, 2, 4, -4, 10, 8, 2, 10, 4, -8, -6, -8, 2, -8, 8, 6, 8, 8, 2, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 2184, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '2184.g', 'trace_hash': 532466831622638842}

Column	Type
area	numeric
conductor	integer
gens	numeric[]
heights	numeric[]
lmfdb_label	text
ngens	smallint
rank_bounds	smallint[]
real_period	numeric
sha_an	numeric
special_value	numeric
tamagawa_product	integer
torsion_generators	numeric[]
xcoord_integral_points	numeric[]

ec_mwbsd • Show schema

{'area': {'__RealLiteral__': 0, 'data': '0.66235531335806204415809120861', 'prec': 103}, 'conductor': 2184, 'gens': [], 'heights': [], 'lmfdb_label': '2184.g2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.7201652113124832638760722818', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7201652113124832638760722817599399109', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2, 0, 1], [10, 0, 1]], 'xcoord_integral_points': [-11, 2, 10]}

Column	Type
iwdata	jsonb
iwp0	smallint
lmfdb_label	text

ec_iwasawa • Show schema
{'iwdata': {'2': 'a', '3': [0, 0], '7': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '2184.g2'}

Column	Type
degree	smallint
field	numeric[]
lmfdb_label	text
torsion	smallint[]

ec_torsion_growth • Show schema

id: 110971
{'degree': 4, 'field': [4, 0, 17, 0, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 4]}
id: 110970
{'degree': 4, 'field': [7, 14, -13, -2, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 4]}
id: 110972
{'degree': 4, 'field': [27, 2, -1, -2, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 4]}
id: 110973
{'degree': 8, 'field': [-48, 0, -272, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 6]}
id: 110975
{'degree': 16, 'field': [27889, 0, -64200, 0, 57928, 0, -26808, 0, 6690, 0, -936, 0, 136, 0, -24, 0, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 8]}
id: 110977
{'degree': 16, 'field': [34225, 0, 44312, 0, 17392, 0, -3384, 0, -2862, 0, -168, 0, 112, 0, 8, 0, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 8]}
id: 110974
{'degree': 16, 'field': [2858788, -2890408, 4105420, -2582536, 1660298, -408160, 77526, 50420, -10267, -5504, 4722, -1580, -40, 112, 4, -8, 1], 'lmfdb_label': '2184.g2', 'torsion': [4, 4]}
id: 110976
{'degree': 16, 'field': [24029604, 0, 13134528, 0, 3728532, 0, 640788, 0, 71053, 0, 5182, 0, 327, 0, 22, 0, 1], 'lmfdb_label': '2184.g2', 'torsion': [2, 8]}

Column	Type
conductor	integer
conductor_valuation	smallint
discriminant_valuation	smallint
j_denominator_valuation	smallint
kodaira_symbol	smallint
lmfdb_label	text
prime	integer
reduction_type	smallint
root_number	smallint
tamagawa_number	smallint

ec_localdata • Show schema

id: 36488
{'conductor': 2184, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2184.g2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
id: 36489
{'conductor': 2184, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2184.g2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
id: 36490
{'conductor': 2184, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2184.g2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
id: 36491
{'conductor': 2184, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2184.g2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}

Column	Type
adelic_gens	bigint[]
adelic_image	text
conductor	integer
elladic_image	text
lmfdb_label	text
modell_image	text
prime	smallint

ec_galrep • Show schema

id: 1678193
{'adelic_gens': [[1, 0, 4, 1], [1683, 2, 334, 2183], [1, 4, 0, 1], [549, 4, 1094, 3], [2181, 4, 2180, 5], [1457, 2, 0, 1], [1093, 4, 2, 9], [1249, 2, 0, 1]], 'adelic_image': '2184.48.0.?', 'conductor': 2184, 'lmfdb_label': '2184.g2', 'prime': 0}
id: 10773
{'conductor': 2184, 'elladic_image': '8.12.0.1', 'lmfdb_label': '2184.g2', 'modell_image': '2Cs', 'prime': 2}

lmfdb_iso 2184.g does not appear in ec_padic

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