LMFDB - Elliptic curve data

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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': '448b', 'Clabel': '448b3', 'Cnumber': 3, 'abc_quality': 1.0465382471182303, 'absD': 917504, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, -1196, -15920], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 448, 'degree': 128, 'elladic_images': ['8.24.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.34454076348138516636207252373', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [1443468546, 7], 'lmfdb_iso': '448.e', 'lmfdb_label': '448.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -299, 1990], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.p.1.3', '56.48.0-56.bp.1.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.2764343071889022423702614513', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 7], [7, 8, 64]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63741774231187068864567298167', 'prec': 107}, 'szpiro_ratio': 5.3849189619893, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [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, 0, 0, -2, 0, 1, 0, -3, 0, -4, 0, -2, 0, 0, 0, -6, 0, 8, 0], 'aplist': [0, 0, -2, 1, -4, -2, -6, 8, 0, -6, -8, 2, 2, -4, 8, -6, 0, 6, -4, 8, 10, -16, 8, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 448, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '448.e', 'trace_hash': 823669738576213693}

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': '0.50203696478935907640370311072', 'prec': 103}, 'conductor': 448, 'gens': [[124, 1320, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2764343071889022423702614513', 'prec': 100}], 'lmfdb_label': '448.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.81183334631051366173246314861', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7358759869411248186869537580981290600', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-20, 0, 1]], 'xcoord_integral_points': [-20, 124]}

Column	Type
iwdata	jsonb
iwp0	smallint
lmfdb_label	text

ec_iwasawa • Show schema

{'iwdata': {'2': 'a', '3': [3, 1, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '448.e1'}

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

ec_torsion_growth • Show schema

id: 19758
{'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 2]}
id: 19760
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [4]}
id: 19759
{'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [4]}
id: 19762
{'degree': 4, 'field': [-14, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 4]}
id: 19761
{'degree': 4, 'field': [49, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 4]}
id: 19766
{'degree': 8, 'field': [-3, 0, -6, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [6]}
id: 19764
{'degree': 8, 'field': [4, 16, 6, -24, 18, -8, 3, -2, 1], 'lmfdb_label': '448.e1', 'torsion': [8]}
id: 19765
{'degree': 8, 'field': [49, 0, 28, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [8]}
id: 19763
{'degree': 8, 'field': [169, 0, 172, 0, -22, 0, 4, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [4, 4]}
id: 19767
{'degree': 16, 'field': [16, 0, -32, 0, 32, 0, -88, 0, 161, 0, -44, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 8]}
id: 19768
{'degree': 16, 'field': [16, 0, 0, 0, -143, 0, 0, 0, 339, 0, 0, 0, -13, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 8]}
id: 19772
{'degree': 16, 'field': [144, 0, 0, 0, 1008, 0, 0, 0, 120, 0, 0, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [12]}
id: 19770
{'degree': 16, 'field': [196, 0, -616, 0, 988, 0, -712, 0, -416, 0, 92, 0, 16, 0, -10, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 6]}
id: 19769
{'degree': 16, 'field': [196, 0, 0, 0, -1568, 0, 0, 0, -420, 0, 0, 0, -112, 0, 0, 0, 1], 'lmfdb_label': '448.e1', 'torsion': [2, 8]}
id: 19771
{'degree': 16, 'field': [322, -2408, 9132, -13192, 13418, -3348, -2468, 3100, -1164, -80, 82, 108, -64, -16, 24, -8, 1], 'lmfdb_label': '448.e1', 'torsion': [12]}

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: 4764
{'conductor': 448, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '448.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
id: 4765
{'conductor': 448, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '448.e1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}

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: 1667763
{'adelic_gens': [[49, 8, 48, 9], [24, 3, 29, 2], [1, 0, 8, 1], [48, 13, 45, 16], [1, 4, 4, 17], [7, 6, 50, 51], [32, 55, 29, 42], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 448, 'lmfdb_label': '448.e1', 'prime': 0}
id: 1955
{'conductor': 448, 'elladic_image': '8.24.0.60', 'lmfdb_label': '448.e1', 'modell_image': '2B', 'prime': 2}

Column	Type
lmfdb_iso	text
p	smallint
prec	smallint
unit	numeric
val	smallint

ec_padic • Show schema

id: 6478
{'lmfdb_iso': '448.e', 'p': 5, 'prec': 20, 'unit': 3939248071437, 'val': 1}
id: 6477
{'lmfdb_iso': '448.e', 'p': 11, 'prec': 20, 'unit': 11519404534210648913, 'val': 1}
id: 6484
{'lmfdb_iso': '448.e', 'p': 13, 'prec': 20, 'unit': 365542586286747368, 'val': 2}
id: 6486
{'lmfdb_iso': '448.e', 'p': 17, 'prec': 20, 'unit': 168563034468757130639783, 'val': 1}
id: 6487
{'lmfdb_iso': '448.e', 'p': 19, 'prec': 20, 'unit': 416687839586044907793264, 'val': 1}
id: 6483
{'lmfdb_iso': '448.e', 'p': 29, 'prec': 20, 'unit': 2334525100792377250577648914, 'val': 1}
id: 6480
{'lmfdb_iso': '448.e', 'p': 31, 'prec': 20, 'unit': 8628857519371855149483063307, 'val': 1}
id: 6494
{'lmfdb_iso': '448.e', 'p': 37, 'prec': 20, 'unit': 572837885068115837556818355955, 'val': 1}
id: 6481
{'lmfdb_iso': '448.e', 'p': 41, 'prec': 20, 'unit': 616637057558985056696426256558, 'val': 1}
id: 6482
{'lmfdb_iso': '448.e', 'p': 43, 'prec': 20, 'unit': 7378368516595481848709355449452, 'val': 1}
id: 6485
{'lmfdb_iso': '448.e', 'p': 47, 'prec': 20, 'unit': 9865327354091872377620303707323, 'val': 1}
id: 6488
{'lmfdb_iso': '448.e', 'p': 53, 'prec': 20, 'unit': 388741426325728983392299547761374, 'val': 1}
id: 6493
{'lmfdb_iso': '448.e', 'p': 61, 'prec': 20, 'unit': 6352285742564239659485056642618488, 'val': 1}
id: 6476
{'lmfdb_iso': '448.e', 'p': 67, 'prec': 20, 'unit': 2836162561630575471828131497005109, 'val': 1}
id: 6479
{'lmfdb_iso': '448.e', 'p': 71, 'prec': 20, 'unit': 62527083443691607759237056129787032, 'val': 1}
id: 6489
{'lmfdb_iso': '448.e', 'p': 73, 'prec': 20, 'unit': 186878963408208825531874772054464258, 'val': 1}
id: 6492
{'lmfdb_iso': '448.e', 'p': 79, 'prec': 20, 'unit': 982570524121878337435774619093099832, 'val': 1}
id: 6490
{'lmfdb_iso': '448.e', 'p': 83, 'prec': 20, 'unit': 1078742382337335011397340721762669611, 'val': 1}
id: 6491
{'lmfdb_iso': '448.e', 'p': 89, 'prec': 20, 'unit': 10837656028004276466243448156450853250, 'val': 1}
id: 6475
{'lmfdb_iso': '448.e', 'p': 97, 'prec': 20, 'unit': 39166778048282752111881749239156730603, 'val': 1}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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