LMFDB - Elliptic curve data

Formats: - HTML - YAML - JSON - 2025-12-07T08:22:18.525155

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': '110670cp', 'Clabel': '110670cp6', 'Cnumber': 6, 'abc_quality': 1.0263485391766844, 'absD': 16398477508430925116750756250000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 177072, 'ainvs': [1, 0, 0, -16306945780, -777467273017600], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 394264576, 'elladic_images': ['8.96.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [479558500651862026155270257138637121, 16398477508430925116750756250000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -16306945780, -777467273017600], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.1', '8.96.0-8.l.1.1', '84.48.0.?', '168.192.1.?', '816.192.2.?', '1488.192.2.?', '1904.192.2.?', '3472.192.2.?', '5712.384.5.?', '8432.192.1.?', '10416.384.5.?', '25296.384.5.?', '59024.384.5.?', '177072.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'szpiro_ratio': 7.073875895013549, '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, 1, -2, 1, 1, 1, 1, 1, 4, 1], 'aplist': [1, 1, 1, 1, -4, -2, 1, 4, 8, -2, -1, 6, 10, -4, 0, 6, 12, -2, 4, -8, 10, 0, -12, -6, -14], 'class_deg': 16, 'class_size': 8, 'conductor': 110670, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 4, 8], [16, 1, 8, 4, 2, 4, 16, 8], [2, 8, 1, 2, 4, 8, 2, 4], [4, 4, 2, 1, 2, 4, 4, 2], [8, 2, 4, 2, 1, 2, 8, 4], [16, 4, 8, 4, 2, 1, 16, 8], [4, 16, 2, 4, 8, 16, 1, 8], [8, 8, 4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '110670.cm', 'trace_hash': 2030220627107999368}

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': '0.000073153143498685829206100517453', 'prec': 117}, 'conductor': 110670, 'gens': [], 'heights': [], 'lmfdb_label': '110670.cm3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.013388051622470122650067948648', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8546824307047027968347897078939887998', 'prec': 130}, 'tamagawa_product': 2048, 'torsion_generators': [[-63040, 31520, 1], [146960, -73480, 1]], 'xcoord_integral_points': [-63040, 146960]}

Column	Type
iwdata	jsonb
iwp0	smallint
lmfdb_label	text

ec_iwasawa • Show schema

{'iwdata': {'2': [14, 2], '3': [1, 0], '5': [1, 0], '7': [5, 0], '17': [1, 0], '31': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '110670.cm3'}

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

ec_torsion_growth • Show schema

id: 5094398
{'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 4]}
id: 5094397
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 4]}
id: 5094396
{'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 4]}
id: 5094401
{'degree': 4, 'field': [-84, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 8]}
id: 5094402
{'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 8]}
id: 5094399
{'degree': 4, 'field': [25, 0, 11, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [4, 4]}
id: 5094400
{'degree': 4, 'field': [25, 10, 12, -2, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 8]}
id: 5094403
{'degree': 4, 'field': [441, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 8]}
id: 5094407
{'degree': 8, 'field': [-531723, 0, -69208, 0, -2526, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 6]}
id: 5094404
{'degree': 8, 'field': [25, 10, 2, -26, 19, -10, 8, -4, 1], 'lmfdb_label': '110670.cm3', 'torsion': [4, 8]}
id: 5094405
{'degree': 8, 'field': [484, 0, -248, 0, 48, 0, 4, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [4, 8]}
id: 5094406
{'degree': 8, 'field': [625, 0, 0, 0, 71, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [4, 8]}
id: 5094408
{'degree': 16, 'field': [289, -2516, 10952, -12868, 7886, -1600, 1560, -2460, 2095, -960, 360, -220, 134, -76, 32, -8, 1], 'lmfdb_label': '110670.cm3', 'torsion': [8, 8]}
id: 5094414
{'degree': 16, 'field': [4665600, 0, -42086400, 0, 31187200, 0, 3904235904, 0, 94593312, 0, 592384, 0, 7296, 0, 168, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 12]}
id: 5094416
{'degree': 16, 'field': [844774225, 466202600, 128640800, -35419120, 10005780, 6318740, 2705952, -896008, 129586, 20064, 20488, -7816, 1424, -84, 32, -8, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 12]}
id: 5094410
{'degree': 16, 'field': [7874993436, -12636279024, 7544731848, -1913154768, 1016512098, -1422942360, 786965844, -114816504, -58431497, 23858348, -2579654, 10976, -2177, 896, -158, -4, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 16]}
id: 5094415
{'degree': 16, 'field': [951690078693, -91389080376, 96447502656, -10207046040, 5327063922, -262547208, 77390140, 9937744, -4088757, 1118072, -272692, 27456, -5122, 224, -12, -8, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 12]}
id: 5094412
{'degree': 16, 'field': [2821109907456, 0, 0, 0, 0, 0, 0, 0, 1267569, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 16]}
id: 5094409
{'degree': 16, 'field': [9670357207480, 4958293915360, 2443368479256, -109282162528, 98818778408, 686869344, 899341156, 417224908, 30252825, 2300332, 114940, -17892, 2366, 644, -72, -8, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 16]}
id: 5094411
{'degree': 16, 'field': [2478758911082496, 0, 0, 0, 0, 0, 0, 0, 37573249, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 16]}
id: 5094413
{'degree': 16, 'field': [548652275911950336, 0, 0, 0, 0, 0, 0, 0, 558997929, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '110670.cm3', 'torsion': [2, 16]}

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: 2720486
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '110670.cm3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
id: 2720487
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '110670.cm3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
id: 2720488
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '110670.cm3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
id: 2720489
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '110670.cm3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
id: 2720490
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '110670.cm3', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
id: 2720491
{'conductor': 110670, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '110670.cm3', 'prime': 31, '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: 2388785
{'adelic_gens': [[1, 16, 6, 110767], [1, 16, 0, 1], [126489, 16, 50786, 345], [118049, 16, 6, 97], [177057, 16, 177056, 17], [1, 0, 16, 1], [1, 16, 0, 132805], [45697, 8, 0, 1], [104169, 8, 41620, 177033], [1, 16, 4, 65]], 'adelic_image': '177072.768.13.?', 'conductor': 110670, 'lmfdb_label': '110670.cm3', 'prime': 0}
id: 439148
{'conductor': 110670, 'elladic_image': '8.96.0.60', 'lmfdb_label': '110670.cm3', 'modell_image': '2Cs', 'prime': 2}

lmfdb_iso 110670.cm 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.