LMFDB - Elliptic curve data

Formats: - HTML - YAML - JSON - 2025-04-04T12:27:35.551997

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
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
stable_faltings_height	numeric
szpiro_ratio	double precision
torsion	smallint
torsion_primes	smallint[]
torsion_structure	smallint[]

ec_curvedata • Show schema

{'Ciso': '3360x', 'Clabel': '3360x1', 'Cnumber': 1, 'abc_quality': 1.0964009209698897, 'absD': 5859137025000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 1, 0, -6378750, -6202979352], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3360, 'degree': 107520, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4134139676079163624642537069', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [448487713888272974160064, 91549016015625], 'lmfdb_iso': '3360.x', 'lmfdb_label': '3360.x3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -6378750, 6202979352], 'min_quad_twist_disc': -4, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '24.24.0-24.a.1.4', '28.24.0-28.a.1.1', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 1120], [5, 6, 672], [7, 8, 160]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0668403773279437077556376462', 'prec': 100}, 'szpiro_ratio': 7.219365047334829, '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, 1, 0, -1, 0, 1, 0, 4, 0, -6, 0, 1, 0, 6, 0, 4, 0], 'aplist': [0, 1, 1, -1, 4, -6, 6, 4, 4, -2, -8, 6, 6, -8, 0, 6, 4, 10, -8, -12, -14, 16, 12, 14, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 3360, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3360.x', 'trace_hash': 3162156426479573}

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': '0.0080118952514981572467045581055', 'prec': 110}, 'conductor': 3360, 'gens': [], 'heights': [], 'lmfdb_label': '3360.x3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.094998261797797567417917703320', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6599513303383318877016956929486910009', 'prec': 130}, 'tamagawa_product': 448, 'torsion_generators': [[-1458, 0, 1], [2916, 0, 1]], 'xcoord_integral_points': [-1459, -1458, 2916]}

Column	Type
iwdata	jsonb
iwp0	smallint
lmfdb_label	text

ec_iwasawa • Show schema
{'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [2, 0]}, 'iwp0': 11, 'lmfdb_label': '3360.x3'}

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

ec_torsion_growth • Show schema

id: 175756
{'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 4]}
id: 175757
{'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 4]}
id: 175758
{'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 4]}
id: 175761
{'degree': 8, 'field': [-3, 0, -232, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 6]}
id: 175760
{'degree': 8, 'field': [81, 0, 108, 0, 78, 0, 12, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 8]}
id: 175759
{'degree': 8, 'field': [106, 148, -106, -92, 67, -28, 14, -4, 1], 'lmfdb_label': '3360.x3', 'torsion': [4, 4]}
id: 175762
{'degree': 16, 'field': [49, -392, 1568, -3920, 6720, -8176, 7168, -4648, 2578, -1576, 1024, -496, 192, -80, 32, -8, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 8]}
id: 175764
{'degree': 16, 'field': [1476225, 0, 1968300, 0, 656100, 0, -65124, 0, -28998, 0, 1836, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '3360.x3', 'torsion': [2, 12]}
id: 175763
{'degree': 16, 'field': [35605089, 0, -31949640, 0, 11237292, 0, -2174904, 0, 283590, 0, -25272, 0, 1644, 0, -72, 0, 1], 'lmfdb_label': '3360.x3', '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: 61363
{'conductor': 3360, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3360.x3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
id: 61364
{'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '3360.x3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
id: 61365
{'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3360.x3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
id: 61366
{'conductor': 3360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3360.x3', 'prime': 7, '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: 1685882
{'adelic_gens': [[87, 2, 166, 167], [45, 4, 8, 11], [73, 2, 0, 1], [1, 4, 0, 1], [1, 0, 4, 1], [3, 2, 110, 167], [165, 4, 164, 5]], 'adelic_image': '168.48.0.?', 'conductor': 3360, 'lmfdb_label': '3360.x3', 'prime': 0}
id: 16874
{'conductor': 3360, 'elladic_image': '4.12.0.1', 'lmfdb_label': '3360.x3', 'modell_image': '2Cs', 'prime': 2}

lmfdb_iso 3360.x does not appear in ec_padic

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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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.