Elliptic curve data - 1225.b2

Formats: - HTML - YAML - JSON - 2023-12-11T13:30:37.696970

• 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': '1225h', 'Clabel': '1225h1', 'Cnumber': 1, 'absD': 6125, 'adelic_genus': 97, 'adelic_index': 2736, 'adelic_level': 5180, 'ainvs': [1, 1, 1, -8, 6], 'analytic_rank': 1, 'bad_primes': [5, 7], 'class_deg': 37, 'class_size': 2, 'cm': 0, 'conductor': 1225, 'degree': 48, 'elladic_images': ['37.114.4.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.53497422781474375918341356667', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 37], 'jinv': [-9317, 1], 'lmfdb_iso': '1225.b', 'lmfdb_label': '1225.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -8, 6], 'min_quad_twist_disc': 1, 'modell_images': ['37B.8.1'], 'modm_images': ['20.2.0.a.1', '37.114.4.b.1', '148.228.10.?', '185.228.10.?', '259.342.16.?', '740.456.25.?', '1036.684.40.?', '1295.1368.40.?', '5180.2736.97.?'], 'nonmax_primes': [37], 'nonmax_rad': 37, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.17505957779114896685301051798', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2616520640991544036844955239', '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, -1, -1, -1, 0, 1, 0, 3, -2, 0, 0, 1, 2, 0, 0, -1, 2, 2, -6, 0], 'aplist': [-1, -1, 0, 0, 0, 2, 2, -6, 3, 7, -2, 8, -5, -7, 0, -6, -10, -7, 5, -2, -6, -2, -11, -9, -16], 'class_deg': 37, 'class_size': 2, 'conductor': 1225, 'isogeny_matrix': [[1, 37], [37, 1]], 'lmfdb_iso': '1225.b', 'trace_hash': 1303089606466468359}
• 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': '2.9152292324486212149200269891', 'prec': 100}, 'conductor': 1225, 'gens': [[0, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.17505957779114896685301051798', 'prec': 103}], 'lmfdb_label': '1225.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.1353485680374347938775159781', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4478647486797316047223462949148971894', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [0, 1, 10]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [1, 0], '5': 'a', '7': 'a', '11': [1, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1225.b2'}
• ec_torsion_growth •

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

  
  
  • id: 60903
    {'degree': 3, 'field': [-13, 5, -1, 1], 'lmfdb_label': '1225.b2', 'torsion': [2]}
  • id: 60904
    {'degree': 6, 'field': [20, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '1225.b2', 'torsion': [2, 2]}
  • id: 60905
    {'degree': 8, 'field': [-469, -539, -55, -16, 109, -1, -5, -4, 1], 'lmfdb_label': '1225.b2', 'torsion': [3]}
  • id: 60906
    {'degree': 12, 'field': [-3520, -3840, 2320, 4240, -444, -2272, -435, 613, 319, 2, -25, -3, 1], 'lmfdb_label': '1225.b2', 'torsion': [4]}
  • id: 60907
    {'degree': 12, 'field': [1, 8, -40, -46, 110, 71, -113, -43, 54, 11, -12, -1, 1], 'lmfdb_label': '1225.b2', 'torsion': [37]}
• 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: 18081
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1225.b2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 18082
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1225.b2', 'prime': 7, '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

  
  
  • id: 1672274
    {'adelic_gens': [[101, 2072, 148, 2157], [1, 3256, 0, 1], [1, 0, 148, 1], [117, 2442, 37, 4323], [1, 0, 148, 3221], [1037, 0, 0, 2073], [1925, 3256, 1924, 1925], [4441, 0, 0, 3701], [1, 30, 0, 1], [75, 74, 1591, 2295], [1, 2590, 0, 1], [2591, 2590, 2590, 2591], [4848, 2923, 4477, 1259], [1, 0, 2590, 1]], 'adelic_image': '5180.2736.97.?', 'conductor': 1225, 'lmfdb_label': '1225.b2', 'prime': 0}
  • id: 5866
    {'conductor': 1225, 'elladic_image': '37.114.4.1', 'lmfdb_label': '1225.b2', 'modell_image': '37B.8.1', 'prime': 37}
• ec_padic •

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

  
  
  • id: 30442
    {'lmfdb_iso': '1225.b', 'p': 13, 'prec': 20, 'unit': 1170024785491982935067, 'val': 1}
  • id: 30444
    {'lmfdb_iso': '1225.b', 'p': 17, 'prec': 20, 'unit': 48373951963768499228631, 'val': 1}
  • id: 30434
    {'lmfdb_iso': '1225.b', 'p': 19, 'prec': 20, 'unit': 1567439762564796576563706, 'val': 1}
  • id: 30448
    {'lmfdb_iso': '1225.b', 'p': 23, 'prec': 20, 'unit': 21306983831082327221835653, 'val': 1}
  • id: 30441
    {'lmfdb_iso': '1225.b', 'p': 29, 'prec': 20, 'unit': 2950635465200619648140982316, 'val': 1}
  • id: 30452
    {'lmfdb_iso': '1225.b', 'p': 31, 'prec': 20, 'unit': 6663502714589732732168511448, 'val': 1}
  • id: 30437
    {'lmfdb_iso': '1225.b', 'p': 37, 'prec': 20, 'unit': 473912372682285970954476131577, 'val': 1}
  • id: 30439
    {'lmfdb_iso': '1225.b', 'p': 41, 'prec': 20, 'unit': 3033099148378738450707288005024, 'val': 1}
  • id: 30440
    {'lmfdb_iso': '1225.b', 'p': 43, 'prec': 20, 'unit': 5719511974537133870640625292240, 'val': 1}
  • id: 30446
    {'lmfdb_iso': '1225.b', 'p': 53, 'prec': 20, 'unit': 478206155339936343061320664249229, 'val': 1}
  • id: 30450
    {'lmfdb_iso': '1225.b', 'p': 59, 'prec': 20, 'unit': 3469575287078879176235216104325373, 'val': 1}
  • id: 30451
    {'lmfdb_iso': '1225.b', 'p': 61, 'prec': 20, 'unit': 103458684544352946878564836545364, 'val': 2}
  • id: 30436
    {'lmfdb_iso': '1225.b', 'p': 67, 'prec': 20, 'unit': 36890639000925101629055705533599879, 'val': 1}
  • id: 30438
    {'lmfdb_iso': '1225.b', 'p': 71, 'prec': 20, 'unit': 94830172830808883661157789747613433, 'val': 1}
  • id: 30447
    {'lmfdb_iso': '1225.b', 'p': 73, 'prec': 20, 'unit': 1702468563444088136285116640348431, 'val': 2}
  • id: 30443
    {'lmfdb_iso': '1225.b', 'p': 79, 'prec': 20, 'unit': 281143058608669751302810778105825883, 'val': 1}
  • id: 30445
    {'lmfdb_iso': '1225.b', 'p': 83, 'prec': 20, 'unit': 2082528562907168957793434664416305383, 'val': 1}
  • id: 30449
    {'lmfdb_iso': '1225.b', 'p': 89, 'prec': 20, 'unit': 8364856548503296113604785419995593612, 'val': 1}
  • id: 30435
    {'lmfdb_iso': '1225.b', 'p': 97, 'prec': 20, 'unit': 35674151692040457213614410097514312552, 'val': 1}