Elliptic curve data - 285.a1

Formats: - HTML - YAML - JSON - 2026-05-17T17:48:04.041671

• 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': '285a', 'Clabel': '285a2', 'Cnumber': 2, 'abc_quality': 1.0317978744296175, 'absD': 28048275, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1140, 'ainvs': [1, 0, 0, -76, -19], 'analytic_rank': 1, 'bad_primes': [3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 285, 'degree': 80, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.11864263774689362441543696896', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [48587168449, 28048275], 'lmfdb_iso': '285.a', 'lmfdb_label': '285.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -76, -19], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.c.1', '76.6.0.?', '1140.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.13482717795889418687569402828', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 2, 19], [3, 4, 95], [5, 6, 19], [19, 20, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.11864263774689362441543696896', 'prec': 103}, 'szpiro_ratio': 4.353237047353329, '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, -1, 1, -1, -1, -1, -2, 3, 1, 1, -6, -1, 0, 2, -1, -1, -6, -1, 1, 1], 'aplist': [-1, 1, -1, -2, -6, 0, -6, 1, -8, 4, 0, 4, 0, -2, -8, 2, 12, 2, -8, 16, 14, 8, 0, 0, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 285, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '285.a', 'trace_hash': 666118259663023950}
• 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': '0.78876624024016080267456130893', 'prec': 103}, 'conductor': 285, 'gens': [[-7, 17, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.13482717795889418687569402828', 'prec': 103}], 'lmfdb_label': '285.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7646479000603136596285790851', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1896124822811041685624781611204499570', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[-1, 1, 2]], 'xcoord_integral_points': [-7, -4, -1, 11, 20, 61, 101]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 3, 0], '37': [1, 0], '41': [1, 3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '285.a1'}
• ec_torsion_growth •

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

  
  
  • id: 11840
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '285.a1', 'torsion': [2, 2]}
  • id: 11841
    {'degree': 4, 'field': [19, 0, 4, 0, 1], 'lmfdb_label': '285.a1', 'torsion': [4]}
  • id: 11843
    {'degree': 8, 'field': [-2727, -2916, 48, 780, 202, -52, -16, -4, 1], 'lmfdb_label': '285.a1', 'torsion': [2, 4]}
  • id: 11844
    {'degree': 8, 'field': [-15, -48, 30, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '285.a1', 'torsion': [6]}
  • id: 11842
    {'degree': 8, 'field': [1581, -1800, 127, 22, 164, 52, -1, -2, 1], 'lmfdb_label': '285.a1', 'torsion': [2, 4]}
  • id: 11846
    {'degree': 16, 'field': [384405, -817194, 1567935, -1663846, 1153958, -160734, -295781, 247708, -1515, -33660, 165, 3504, -493, -70, 30, -8, 1], 'lmfdb_label': '285.a1', 'torsion': [2, 6]}
  • id: 11845
    {'degree': 16, 'field': [275759236, 0, 103817824, 0, 36484465, 0, 6065161, 0, 471979, 0, 13756, 0, 415, 0, 19, 0, 1], 'lmfdb_label': '285.a1', 'torsion': [8]}
• 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: 2562
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '285.a1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 2563
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '285.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2564
    {'conductor': 285, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '285.a1', 'prime': 19, '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: 1666936
    {'adelic_gens': [[1, 2, 2, 5], [856, 289, 285, 856], [1, 4, 0, 1], [457, 4, 914, 9], [1137, 4, 1136, 5], [422, 1, 359, 0], [1, 0, 4, 1], [3, 4, 8, 11], [761, 4, 382, 9]], 'adelic_image': '1140.12.0.?', 'conductor': 285, 'lmfdb_label': '285.a1', 'prime': 0}
  • id: 1155
    {'conductor': 285, 'elladic_image': '2.3.0.1', 'lmfdb_label': '285.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2820
    {'lmfdb_iso': '285.a', 'p': 7, 'prec': 20, 'unit': 2361010940967383, 'val': 1}
  • id: 2818
    {'lmfdb_iso': '285.a', 'p': 11, 'prec': 20, 'unit': 1697255156687471137, 'val': 1}
  • id: 2825
    {'lmfdb_iso': '285.a', 'p': 17, 'prec': 20, 'unit': 158319416037158208483886, 'val': 1}
  • id: 2829
    {'lmfdb_iso': '285.a', 'p': 23, 'prec': 20, 'unit': 40936968974196744944193451, 'val': 1}
  • id: 2823
    {'lmfdb_iso': '285.a', 'p': 29, 'prec': 20, 'unit': 1291906551247099267435904190, 'val': 1}
  • id: 2819
    {'lmfdb_iso': '285.a', 'p': 37, 'prec': 20, 'unit': 545416845455761467135891171006, 'val': 1}
  • id: 2822
    {'lmfdb_iso': '285.a', 'p': 43, 'prec': 20, 'unit': 10094220869652299247610977858999, 'val': 1}
  • id: 2831
    {'lmfdb_iso': '285.a', 'p': 47, 'prec': 20, 'unit': 3054256445268753537728053268154, 'val': 1}
  • id: 2827
    {'lmfdb_iso': '285.a', 'p': 53, 'prec': 20, 'unit': 102280588569900699866304873705287, 'val': 1}
  • id: 2828
    {'lmfdb_iso': '285.a', 'p': 59, 'prec': 20, 'unit': 2581496512415726104754887685651756, 'val': 1}
  • id: 2832
    {'lmfdb_iso': '285.a', 'p': 61, 'prec': 20, 'unit': 7989223268274700785370635932038186, 'val': 1}
  • id: 2826
    {'lmfdb_iso': '285.a', 'p': 67, 'prec': 20, 'unit': 34272171352947694392685116207289861, 'val': 1}
  • id: 2830
    {'lmfdb_iso': '285.a', 'p': 71, 'prec': 20, 'unit': 83983316234788933720879797549224255, 'val': 1}
  • id: 2821
    {'lmfdb_iso': '285.a', 'p': 73, 'prec': 20, 'unit': 136153705404032745116054302809842248, 'val': 1}
  • id: 2824
    {'lmfdb_iso': '285.a', 'p': 79, 'prec': 20, 'unit': 515726054206696402605696617708050013, 'val': 1}
  • id: 2817
    {'lmfdb_iso': '285.a', 'p': 97, 'prec': 20, 'unit': 55363371147098332050889226503425570575, 'val': 1}