Elliptic curve data - 1805.a1

Formats: - HTML - YAML - JSON - 2023-01-27T07:03:25.663291

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1805a', 'Clabel': '1805a2', 'Cnumber': 2, 'absD': 33171021564453125, 'adelic_genus': 2, 'adelic_index': 144, 'adelic_level': 1710, 'ainvs': [0, 1, 1, -105171, -9810339], 'analytic_rank': 1, 'bad_primes': [5, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 1805, 'degree': 14364, 'elladic_images': ['9.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8792998366576829268337916840', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [7575076864, 1953125], 'lmfdb_iso': '1805.a', 'lmfdb_label': '1805.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -105171, -9810339], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.2'], 'modm_images': ['1.1.0.1', '3.8.0.2', '9.24.0.4', '10.2.0.1', '30.16.0.4', '90.48.0.?', '171.72.0.?', '1710.144.2.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8017918040879408639542608313', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.083659482786610713172226603924', 'prec': 110}, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, -2, -1, 0, -4, 0, 1, 0, 3, 4, 2, 0, 2, 4, 6, 0, 0, 2], 'aplist': [0, -2, -1, -4, 3, 2, 6, 0, 0, -3, -7, 8, -6, -4, 6, -6, -15, 5, 2, -3, 8, 5, 12, -15, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 1805, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '1805.a', 'trace_hash': 528242284348825028}
• 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': '0.023316368057237509545090247857', 'prec': 107}, 'conductor': 1805, 'gens': [[-241, 1263, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8017918040879408639542608313', 'prec': 100}], 'lmfdb_label': '1805.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27016308125805859301102556692', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4603328767337430698402491790108626644', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [-241]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 1, 0], '3': [3, 1], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': 'a', '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': '1805.a1'}
• ec_torsion_growth •

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

  
  
  • id: 92027
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1805.a1', 'torsion': [3]}
  • id: 92029
    {'degree': 3, 'field': [-12, -6, -1, 1], 'lmfdb_label': '1805.a1', 'torsion': [3]}
  • id: 92028
    {'degree': 3, 'field': [45, -25, -1, 1], 'lmfdb_label': '1805.a1', 'torsion': [2]}
  • id: 92030
    {'degree': 6, 'field': [-369, -183, 158, 49, -22, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [2, 2]}
  • id: 92031
    {'degree': 6, 'field': [12, 6, -5, -3, 4, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [3, 3]}
  • id: 92032
    {'degree': 6, 'field': [49, -175, 632, 11, 26, -1, 1], 'lmfdb_label': '1805.a1', 'torsion': [6]}
  • id: 92033
    {'degree': 9, 'field': [18, 30, 28, 21, -29, -20, -5, 4, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [6]}
  • id: 92034
    {'degree': 12, 'field': [-8, 48, -400, 1560, -3084, 3504, -2408, 984, -206, 4, 12, -6, 1], 'lmfdb_label': '1805.a1', 'torsion': [4]}
  • id: 92035
    {'degree': 12, 'field': [136161, 67527, 91791, 7248, 25813, 797, 4590, -313, 473, -32, 31, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [2, 6]}
  • id: 92037
    {'degree': 18, 'field': [324, 540, 396, 84, 676, 1968, 1673, 433, 1695, 776, -27, 297, 60, -169, 21, -2, 5, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [3, 6]}
  • id: 92038
    {'degree': 18, 'field': [900, -2520, 1764, 1668, -410, -4274, 6359, -4801, 2051, 120, -1095, 753, -272, 77, 23, -20, 3, -3, 1], 'lmfdb_label': '1805.a1', 'torsion': [2, 6]}
  • id: 92036
    {'degree': 18, 'field': [19683, 0, 0, -13851, 0, 0, 2700, 0, 0, -171, 0, 0, 100, 0, 0, -19, 0, 0, 1], 'lmfdb_label': '1805.a1', 'torsion': [3, 9]}
• 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: 29193
    {'conductor': 1805, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '1805.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 29194
    {'conductor': 1805, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1805.a1', 'prime': 19, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1675845
    {'adelic_gens': [[1, 18, 12, 217], [1, 18, 0, 1], [10, 9, 81, 73], [1, 18, 0, 191], [1693, 18, 1692, 19], [85, 1692, 1152, 1321], [1027, 18, 693, 163], [1, 0, 18, 1], [13, 12, 1646, 1651]], 'adelic_image': '1710.144.2.?', 'conductor': 1805, 'lmfdb_label': '1805.a1', 'prime': 0}
  • id: 8901
    {'conductor': 1805, 'elladic_image': '9.24.0.4', 'lmfdb_label': '1805.a1', 'modell_image': '3B.1.2', 'prime': 3}
• ec_padic •

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

  
  
  • id: 50971
    {'lmfdb_iso': '1805.a', 'p': 7, 'prec': 20, 'unit': 8767557346108738, 'val': 1}
  • id: 50969
    {'lmfdb_iso': '1805.a', 'p': 11, 'prec': 20, 'unit': 25983815218724534641, 'val': 1}
  • id: 50975
    {'lmfdb_iso': '1805.a', 'p': 13, 'prec': 20, 'unit': 749103308506679309873, 'val': 1}
  • id: 50977
    {'lmfdb_iso': '1805.a', 'p': 17, 'prec': 20, 'unit': 126746848232675526886900, 'val': 1}
  • id: 50974
    {'lmfdb_iso': '1805.a', 'p': 29, 'prec': 20, 'unit': 4425355913898098195449673666, 'val': 1}
  • id: 50986
    {'lmfdb_iso': '1805.a', 'p': 31, 'prec': 20, 'unit': 513257744372260490640973390, 'val': 1}
  • id: 50970
    {'lmfdb_iso': '1805.a', 'p': 37, 'prec': 20, 'unit': 224926113293577088215474881421, 'val': 1}
  • id: 50972
    {'lmfdb_iso': '1805.a', 'p': 41, 'prec': 20, 'unit': 2693955051345930605095899565414, 'val': 1}
  • id: 50973
    {'lmfdb_iso': '1805.a', 'p': 43, 'prec': 20, 'unit': 8176511671400293577931229165711, 'val': 1}
  • id: 50984
    {'lmfdb_iso': '1805.a', 'p': 47, 'prec': 20, 'unit': 12630916338188535210396119831357, 'val': 1}
  • id: 50979
    {'lmfdb_iso': '1805.a', 'p': 53, 'prec': 20, 'unit': 433612068015266734113752172091971, 'val': 1}
  • id: 50980
    {'lmfdb_iso': '1805.a', 'p': 59, 'prec': 20, 'unit': 2262593995074699682069336835334623, 'val': 1}
  • id: 50985
    {'lmfdb_iso': '1805.a', 'p': 61, 'prec': 20, 'unit': 3739129258626175693894070452108843, 'val': 1}
  • id: 50978
    {'lmfdb_iso': '1805.a', 'p': 67, 'prec': 20, 'unit': 16768647570513686019774325300456538, 'val': 1}
  • id: 50983
    {'lmfdb_iso': '1805.a', 'p': 71, 'prec': 20, 'unit': 138842267771801525169251927473261870, 'val': 1}
  • id: 50981
    {'lmfdb_iso': '1805.a', 'p': 73, 'prec': 20, 'unit': 211406739509524093616892900238619378, 'val': 1}
  • id: 50976
    {'lmfdb_iso': '1805.a', 'p': 79, 'prec': 20, 'unit': 208887210963175905606351300876460465, 'val': 1}
  • id: 50968
    {'lmfdb_iso': '1805.a', 'p': 83, 'prec': 20, 'unit': 1638477545908825769831262711501633736, 'val': 1}
  • id: 50982
    {'lmfdb_iso': '1805.a', 'p': 89, 'prec': 20, 'unit': 7639351175589828230329914917036534279, 'val': 1}
  • id: 50967
    {'lmfdb_iso': '1805.a', 'p': 97, 'prec': 20, 'unit': 18849831959969887854333570816363691228, 'val': 1}