Elliptic curve data - 1872.e3

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• ec_curvedata •

  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[]

  
  {'Ciso': '1872i', 'Clabel': '1872i1', 'Cnumber': 1, 'abc_quality': 0.9241957238555172, 'absD': 12282192, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 0, 0, -66, 119], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1872, 'degree': 256, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.059284288276828514590387837565', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [2725888, 1053], 'lmfdb_iso': '1872.e', 'lmfdb_label': '1872.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7, 2], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '12.12.0-4.c.1.1', '24.24.0-24.z.1.12', '26.6.0.b.1', '52.12.0.g.1', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3194903778699195727103277851', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 117], [3, 8, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.72107091624387476757964548805', 'prec': 107}, 'szpiro_ratio': 3.209466357406256, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

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

  
  {'anlist': [0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, -2, 0, 0, 1, -2, 4, 0, -6, 0, -2, -6, 12, -4, -6, -8, -2, -4, -12, -14, 0, 8, 18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 1872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1872.e', 'trace_hash': 1311746732148815824}
• ec_mwbsd •

  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[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.88819090449706968046220762957', 'prec': 103}, 'conductor': 1872, 'gens': [[-5, 18, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3194903778699195727103277851', 'prec': 100}], 'lmfdb_label': '1872.e3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.0526958914416500271464839696', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7085124774503742006087399479640825557', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[7, 0, 1]], 'xcoord_integral_points': [-5, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1872.e3'}
• ec_torsion_growth •

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

  
  
  • id: 94861
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [4]}
  • id: 94860
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 2]}
  • id: 94862
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [4]}
  • id: 94863
    {'degree': 4, 'field': [-3, 12, -11, -2, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 4]}
  • id: 94864
    {'degree': 4, 'field': [13, 0, -26, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [8]}
  • id: 94868
    {'degree': 8, 'field': [-117, 144, -288, 42, 12, 12, -10, -2, 1], 'lmfdb_label': '1872.e3', 'torsion': [6]}
  • id: 94866
    {'degree': 8, 'field': [1, 0, -3, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [8]}
  • id: 94867
    {'degree': 8, 'field': [81, 0, -498, 0, 379, 0, -38, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 8]}
  • id: 94865
    {'degree': 8, 'field': [169, 0, 0, 0, 13, 0, 0, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 4]}
  • id: 94873
    {'degree': 16, 'field': [-642758, 1594496, 2059004, -2199140, -4397546, -2095776, 281998, 551216, 111410, -45272, -20252, 1818, 1828, 26, -70, -2, 1], 'lmfdb_label': '1872.e3', 'torsion': [12]}
  • id: 94871
    {'degree': 16, 'field': [-8928, -172224, -654336, 1070784, -624336, 136032, 236016, -162240, -14294, 27300, -2188, -1404, 552, 0, -46, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [16]}
  • id: 94870
    {'degree': 16, 'field': [1, 0, -3, 0, 8, 0, 3, 0, -9, 0, 3, 0, 8, 0, -3, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 8]}
  • id: 94869
    {'degree': 16, 'field': [81, 54, 18, 336, -23, -306, 498, -218, -28, 136, -88, 22, 9, -12, 8, -4, 1], 'lmfdb_label': '1872.e3', 'torsion': [4, 4]}
  • id: 94874
    {'degree': 16, 'field': [6561, 0, -17496, 0, 26244, 0, -16632, 0, 5958, 0, -1848, 0, 324, 0, -24, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [12]}
  • id: 94872
    {'degree': 16, 'field': [59049, 0, 256608, 0, -61884, 0, 57024, 0, 2430, 0, -1056, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '1872.e3', 'torsion': [2, 6]}
• ec_localdata •

  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

  
  
  • id: 30300
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1872.e3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 30301
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '1872.e3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 30302
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1872.e3', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1676205
    {'adelic_gens': [[7, 6, 306, 307], [224, 3, 101, 2], [1, 0, 8, 1], [103, 304, 100, 279], [1, 8, 0, 1], [1, 4, 4, 17], [43, 42, 130, 283], [305, 8, 304, 9], [191, 192, 26, 185]], 'adelic_image': '312.48.0.?', 'conductor': 1872, 'lmfdb_label': '1872.e3', 'prime': 0}
  • id: 9143
    {'conductor': 1872, 'elladic_image': '8.12.0.6', 'lmfdb_label': '1872.e3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 53385
    {'lmfdb_iso': '1872.e', 'p': 5, 'prec': 20, 'unit': 1441094973634, 'val': 2}
  • id: 53378
    {'lmfdb_iso': '1872.e', 'p': 17, 'prec': 20, 'unit': 107662076420009938942970, 'val': 1}
  • id: 53369
    {'lmfdb_iso': '1872.e', 'p': 19, 'prec': 20, 'unit': 680640542565111368088191, 'val': 1}
  • id: 53376
    {'lmfdb_iso': '1872.e', 'p': 29, 'prec': 20, 'unit': 593488398077877079219709821, 'val': 1}
  • id: 53372
    {'lmfdb_iso': '1872.e', 'p': 37, 'prec': 20, 'unit': 208496650407368377913708955556, 'val': 1}
  • id: 53374
    {'lmfdb_iso': '1872.e', 'p': 41, 'prec': 20, 'unit': 1558176412375877769289824465873, 'val': 1}
  • id: 53375
    {'lmfdb_iso': '1872.e', 'p': 43, 'prec': 20, 'unit': 6789964918510116046300429477896, 'val': 1}
  • id: 53377
    {'lmfdb_iso': '1872.e', 'p': 47, 'prec': 20, 'unit': 17396929095682784619516971590434, 'val': 1}
  • id: 53380
    {'lmfdb_iso': '1872.e', 'p': 53, 'prec': 20, 'unit': 190870801973215195180771453981637, 'val': 1}
  • id: 53383
    {'lmfdb_iso': '1872.e', 'p': 59, 'prec': 20, 'unit': 2308422139180611419827007897929318, 'val': 1}
  • id: 53384
    {'lmfdb_iso': '1872.e', 'p': 61, 'prec': 20, 'unit': 8264965710248944194111220800218529, 'val': 1}
  • id: 53371
    {'lmfdb_iso': '1872.e', 'p': 67, 'prec': 20, 'unit': 48785493750139963863436293157429348, 'val': 1}
  • id: 53373
    {'lmfdb_iso': '1872.e', 'p': 71, 'prec': 20, 'unit': 58456679386803409066884305327740848, 'val': 1}
  • id: 53381
    {'lmfdb_iso': '1872.e', 'p': 73, 'prec': 20, 'unit': 92400720231886774220386917952281558, 'val': 1}
  • id: 53379
    {'lmfdb_iso': '1872.e', 'p': 83, 'prec': 20, 'unit': 1751194918910164542314323299936437570, 'val': 1}
  • id: 53382
    {'lmfdb_iso': '1872.e', 'p': 89, 'prec': 20, 'unit': 970282357669959500600329656968653826, 'val': 1}
  • id: 53370
    {'lmfdb_iso': '1872.e', 'p': 97, 'prec': 20, 'unit': 24508108208143714577864732243748790887, 'val': 1}