Elliptic curve data - 2240.b1

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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
  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[]

  
  {'Ciso': '2240v', 'Clabel': '2240v1', 'Cnumber': 1, 'abc_quality': 0.6649105223833719, 'absD': 2240, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 70, 'ainvs': [0, 0, 0, 2, -2], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 2240, 'degree': 192, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.67335748478093139403029036329', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [13824, 35], 'lmfdb_iso': '2240.b', 'lmfdb_label': '2240.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 8, 16], 'min_quad_twist_disc': -8, 'modell_images': [], 'modm_images': ['70.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.75635092438639688715997281835', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 35], [5, 6, 448], [7, 8, 320]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0199310750609040487389064240', 'prec': 103}, 'szpiro_ratio': 1.932718843754542, '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, -3, 0, -1, 0, 1, 0, 6, 0, -3, 0, -1, 0, 3, 0, -1, 0, 4, 0], 'aplist': [0, -3, -1, 1, -3, -1, -1, 4, -4, 9, -6, 8, 6, -8, 7, 8, 4, -10, -8, 12, -14, 5, -16, -14, -17], 'class_deg': 1, 'class_size': 1, 'conductor': 2240, 'isogeny_matrix': [[1]], 'lmfdb_iso': '2240.b', 'trace_hash': 1081460356327870125}
• 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': '3.8447745612025480622754295745', 'prec': 100}, 'conductor': 2240, 'gens': [[1, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.75635092438639688715997281835', 'prec': 103}], 'lmfdb_label': '2240.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.3820051396353339177507476385', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8016317892563332028934673946354773690', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 3, 0], '5': [3, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '2240.b1'}
• ec_torsion_growth •

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

  
  
  • id: 113940
    {'degree': 3, 'field': [-2, 2, 0, 1], 'lmfdb_label': '2240.b1', 'torsion': [2]}
  • id: 113941
    {'degree': 6, 'field': [1, -3, 8, -11, 8, -3, 1], 'lmfdb_label': '2240.b1', 'torsion': [2, 2]}
  • id: 113942
    {'degree': 8, 'field': [-108, 0, -216, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '2240.b1', 'torsion': [3]}
  • id: 113943
    {'degree': 12, 'field': [-875, 0, 18, 0, 427, 0, 64, 0, 3, 0, 6, 0, 1], 'lmfdb_label': '2240.b1', 'torsion': [4]}
• 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: 37624
    {'conductor': 2240, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '2240.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 37625
    {'conductor': 2240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2240.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 37626
    {'conductor': 2240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2240.b1', 'prime': 7, '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

  
  {'adelic_gens': [[69, 2, 68, 3], [1, 2, 0, 1], [31, 2, 31, 3], [1, 0, 2, 1], [57, 2, 57, 3], [1, 1, 69, 0]], 'adelic_image': '70.2.0.?', 'conductor': 2240, 'lmfdb_label': '2240.b1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 67161
    {'lmfdb_iso': '2240.b', 'p': 11, 'prec': 20, 'unit': 30302353658069510396, 'val': 1}
  • id: 67167
    {'lmfdb_iso': '2240.b', 'p': 13, 'prec': 20, 'unit': 67915849246234610252, 'val': 1}
  • id: 67169
    {'lmfdb_iso': '2240.b', 'p': 17, 'prec': 20, 'unit': 39227158453923630219206, 'val': 1}
  • id: 67170
    {'lmfdb_iso': '2240.b', 'p': 19, 'prec': 20, 'unit': 1697782247917875559076483, 'val': 1}
  • id: 67174
    {'lmfdb_iso': '2240.b', 'p': 23, 'prec': 20, 'unit': 48931129410792388916888754, 'val': 1}
  • id: 67166
    {'lmfdb_iso': '2240.b', 'p': 29, 'prec': 20, 'unit': 3180056936100427409594148524, 'val': 1}
  • id: 67179
    {'lmfdb_iso': '2240.b', 'p': 31, 'prec': 20, 'unit': 16469955906023079007520972854, 'val': 1}
  • id: 67162
    {'lmfdb_iso': '2240.b', 'p': 37, 'prec': 20, 'unit': 622718544403831926500968041058, 'val': 1}
  • id: 67164
    {'lmfdb_iso': '2240.b', 'p': 41, 'prec': 20, 'unit': 3638536440529794610145505110567, 'val': 1}
  • id: 67165
    {'lmfdb_iso': '2240.b', 'p': 43, 'prec': 20, 'unit': 1886973570629611719534295663417, 'val': 1}
  • id: 67176
    {'lmfdb_iso': '2240.b', 'p': 47, 'prec': 20, 'unit': 28603524222792847155429013312667, 'val': 1}
  • id: 67171
    {'lmfdb_iso': '2240.b', 'p': 53, 'prec': 20, 'unit': 508878780831285840190207547155965, 'val': 1}
  • id: 67172
    {'lmfdb_iso': '2240.b', 'p': 59, 'prec': 20, 'unit': 1378589282896678096849711066404945, 'val': 1}
  • id: 67177
    {'lmfdb_iso': '2240.b', 'p': 61, 'prec': 20, 'unit': 5711925338068873487553485161990490, 'val': 1}
  • id: 67160
    {'lmfdb_iso': '2240.b', 'p': 67, 'prec': 20, 'unit': 6532250703608121899501735344870195, 'val': 1}
  • id: 67163
    {'lmfdb_iso': '2240.b', 'p': 71, 'prec': 20, 'unit': 13143218782736116487333850645310262, 'val': 1}
  • id: 67173
    {'lmfdb_iso': '2240.b', 'p': 73, 'prec': 20, 'unit': 155824505017290763520279324861730488, 'val': 1}
  • id: 67168
    {'lmfdb_iso': '2240.b', 'p': 79, 'prec': 20, 'unit': 467931548752261672055890169081362707, 'val': 1}
  • id: 67178
    {'lmfdb_iso': '2240.b', 'p': 83, 'prec': 20, 'unit': 575130894070456930609677225703799611, 'val': 1}
  • id: 67175
    {'lmfdb_iso': '2240.b', 'p': 89, 'prec': 20, 'unit': 8808810060237372250262956469897259694, 'val': 1}
  • id: 67159
    {'lmfdb_iso': '2240.b', 'p': 97, 'prec': 20, 'unit': 26506654848126562279757521848817170570, 'val': 1}