Elliptic curve data - 225.c2

Formats: - HTML - YAML - JSON - 2023-06-04T13:06:28.477708

• 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': '225a', 'Clabel': '225a1', 'Cnumber': 1, 'absD': 675, 'ainvs': [0, 0, 1, 0, 1], 'analytic_rank': 1, 'bad_primes': [3, 5], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 225, 'degree': 8, 'elladic_images': ['5.30.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.77822470418866042970759799775', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '225.c', 'lmfdb_label': '225.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 1], 'min_quad_twist_disc': 1, 'modell_images': ['5Ns.2.1'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.15364003501329447809907699066', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, '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, 0, -2, 0, 0, -5, 0, 0, 0, 0, 0, -5, 0, 0, 4, 0, 0, -1, 0], 'aplist': [0, 0, 0, -5, 0, -5, 0, -1, 0, 0, -7, 10, 0, -5, 0, 0, 0, -13, -5, 0, 10, -4, 0, 0, -5], 'class_deg': 3, 'class_size': 2, 'conductor': 225, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '225.c', 'trace_hash': 2140124914231022951}
• 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': '4.7419545753387037738280572794', 'prec': 100}, 'conductor': 225, 'gens': [[1, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.15364003501329447809907699066', 'prec': 103}], 'lmfdb_label': '225.c2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.0529757590368917612716776534', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2453986750529236279151961986275819383', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-1, 1, 11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 3, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 3, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '225.c2'}
• ec_torsion_growth •

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

  
  
  • id: 9488
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [3]}
  • id: 9489
    {'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [2]}
  • id: 9492
    {'degree': 6, 'field': [1, -1, 0, -5, 0, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [6]}
  • id: 9490
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '225.c2', 'torsion': [2, 2]}
  • id: 9491
    {'degree': 6, 'field': [4, 12, 15, -5, 0, -3, 1], 'lmfdb_label': '225.c2', 'torsion': [3]}
  • id: 9493
    {'degree': 8, 'field': [1, 1, -13, 13, -5, 2, 2, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [15]}
  • id: 9494
    {'degree': 12, 'field': [-251, 558, -948, 730, -465, 168, -144, 204, -105, 10, 12, -6, 1], 'lmfdb_label': '225.c2', 'torsion': [4]}
  • id: 9497
    {'degree': 12, 'field': [1, -1, 1, 10, -5, -1, 26, -1, -5, 10, 1, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [2, 6]}
  • id: 9495
    {'degree': 12, 'field': [4, -42, 177, -400, 585, -642, 551, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '225.c2', 'torsion': [3, 3]}
  • id: 9496
    {'degree': 12, 'field': [19, 18, -28, 10, 15, -57, 86, -81, 55, -30, 12, -1, 1], 'lmfdb_label': '225.c2', 'torsion': [7]}
  • id: 9498
    {'degree': 16, 'field': [1, -5, 16, -30, 57, -110, 183, -240, 250, -215, 157, -100, 57, -30, 14, -5, 1], 'lmfdb_label': '225.c2', 'torsion': [5, 15]}
  • id: 9499
    {'degree': 18, 'field': [-1, -24, 0, 117, 315, 36, -921, -1005, 288, 1270, 675, -360, -345, 60, 90, -3, -12, 0, 1], 'lmfdb_label': '225.c2', 'torsion': [9]}
  • id: 9500
    {'degree': 18, 'field': [1, 0, 0, 4, 0, 0, 145, 0, 0, 10, 0, 0, 5, 0, 0, -6, 0, 0, 1], 'lmfdb_label': '225.c2', 'torsion': [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: 1989
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '225.c2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1990
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '225.c2', 'prime': 5, 'reduction_type': 0, '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

  
  {'conductor': 225, 'elladic_image': '5.30.0.2', 'lmfdb_label': '225.c2', 'modell_image': '5Ns.2.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 1818
    {'lmfdb_iso': '225.c', 'p': 7, 'prec': 20, 'unit': 2158029952987845, 'val': 1}
  • id: 1821
    {'lmfdb_iso': '225.c', 'p': 13, 'prec': 20, 'unit': 74712189536028181524, 'val': 1}
  • id: 1823
    {'lmfdb_iso': '225.c', 'p': 19, 'prec': 20, 'unit': 633585264588543671890599, 'val': 1}
  • id: 1825
    {'lmfdb_iso': '225.c', 'p': 31, 'prec': 20, 'unit': 17207376233283168642253676781, 'val': 1}
  • id: 1817
    {'lmfdb_iso': '225.c', 'p': 37, 'prec': 20, 'unit': 584400425203953301136372498262, 'val': 1}
  • id: 1820
    {'lmfdb_iso': '225.c', 'p': 43, 'prec': 20, 'unit': 9224780549909916344082808105179, 'val': 1}
  • id: 1824
    {'lmfdb_iso': '225.c', 'p': 61, 'prec': 20, 'unit': 8308906531020947212034562896244234, 'val': 1}
  • id: 1816
    {'lmfdb_iso': '225.c', 'p': 67, 'prec': 20, 'unit': 32051945030749841303292978425501265, 'val': 1}
  • id: 1819
    {'lmfdb_iso': '225.c', 'p': 73, 'prec': 20, 'unit': 248622483523280619277644832156691320, 'val': 1}
  • id: 1822
    {'lmfdb_iso': '225.c', 'p': 79, 'prec': 20, 'unit': 472448492340657392483784980712851365, 'val': 1}
  • id: 1815
    {'lmfdb_iso': '225.c', 'p': 97, 'prec': 20, 'unit': 44340154612108798911697406016713785570, 'val': 1}