Elliptic curve data - 2304.a2

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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': '2304p', 'Clabel': '2304p1', 'Cnumber': 1, 'absD': 373248, 'ainvs': [0, 0, 0, 18, 0], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': -4, 'conductor': 2304, 'degree': 256, 'elladic_images': ['16.192.9.145'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.24136639615749569049172837375', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [1728, 1], 'lmfdb_iso': '2304.a', 'lmfdb_label': '2304.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 8, 0], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.71474134868387035118438908301', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 6, 256]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3105329259115095182522750833', 'prec': 103}, 'szpiro_ratio': 2.619951566614066, '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, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -4, 0, 0, 4, 2, 0, 0, -4, 0, -12, 10, 0, 0, -4, 0, -12, 0, 0, -6, 0, 0, -10, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 2304, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '2304.a', 'trace_hash': 1151107673569486009}
• 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': '1.6204968379465955055379615141', 'prec': 100}, 'conductor': 2304, 'gens': [[3, 9, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.71474134868387035118438908301', 'prec': 103}], 'lmfdb_label': '2304.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8002759999214539912407190766', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5734633923741266002289673990323402740', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0, 3, 6, 72]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [5, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2304.a2'}
• ec_torsion_growth •

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

  
  
  • id: 116992
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [2, 2]}
  • id: 116993
    {'degree': 4, 'field': [-18, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [4]}
  • id: 116997
    {'degree': 8, 'field': [-12, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [6]}
  • id: 116995
    {'degree': 8, 'field': [7, 40, 64, 24, -26, -16, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [8]}
  • id: 116996
    {'degree': 8, 'field': [79, 80, 88, 24, 10, -8, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [8]}
  • id: 116994
    {'degree': 8, 'field': [81, 0, -108, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [4, 4]}
  • id: 116998
    {'degree': 8, 'field': [1620, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [10]}
  • id: 117002
    {'degree': 16, 'field': [9, 0, 0, 0, 36, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [2, 6]}
  • id: 117000
    {'degree': 16, 'field': [144, 0, 0, 0, 144, 0, 0, 0, 156, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [3, 6]}
  • id: 116999
    {'degree': 16, 'field': [196, -1344, 4608, -8416, 10144, -9568, 7808, -5392, 3044, -1696, 1024, -496, 192, -80, 32, -8, 1], 'lmfdb_label': '2304.a2', 'torsion': [4, 8]}
  • id: 117001
    {'degree': 16, 'field': [104976, 0, 0, 0, 104976, 0, 0, 0, -13284, 0, 0, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [10]}
  • id: 117003
    {'degree': 16, 'field': [164025, 0, 0, 0, -43740, 0, 0, 0, 3726, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '2304.a2', 'torsion': [2, 10]}
• 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: 38685
    {'conductor': 2304, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '2304.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 38686
    {'conductor': 2304, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '2304.a2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  {'conductor': 2304, 'elladic_image': '16.192.9.145', 'lmfdb_label': '2304.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 69434
    {'lmfdb_iso': '2304.a', 'p': 5, 'prec': 20, 'unit': 17798064841449, 'val': 1}
  • id: 69427
    {'lmfdb_iso': '2304.a', 'p': 13, 'prec': 20, 'unit': 121967566613744839500, 'val': 1}
  • id: 69429
    {'lmfdb_iso': '2304.a', 'p': 17, 'prec': 20, 'unit': 94519017124027441594456, 'val': 1}
  • id: 69428
    {'lmfdb_iso': '2304.a', 'p': 29, 'prec': 20, 'unit': 3877529960646586771966622158, 'val': 1}
  • id: 69425
    {'lmfdb_iso': '2304.a', 'p': 37, 'prec': 20, 'unit': 233172947572973346999680704363, 'val': 1}
  • id: 69426
    {'lmfdb_iso': '2304.a', 'p': 41, 'prec': 20, 'unit': 443448256037619171774076212254, 'val': 1}
  • id: 69430
    {'lmfdb_iso': '2304.a', 'p': 53, 'prec': 20, 'unit': 155441396993223416754718092565331, 'val': 1}
  • id: 69433
    {'lmfdb_iso': '2304.a', 'p': 61, 'prec': 20, 'unit': 3783670222082030790786341476805345, 'val': 1}
  • id: 69431
    {'lmfdb_iso': '2304.a', 'p': 73, 'prec': 20, 'unit': 169034935337982850916769353832751427, 'val': 1}
  • id: 69432
    {'lmfdb_iso': '2304.a', 'p': 89, 'prec': 20, 'unit': 983484145976090910598251587874378362, 'val': 1}
  • id: 69424
    {'lmfdb_iso': '2304.a', 'p': 97, 'prec': 20, 'unit': 50939538606378970463881065809117616890, 'val': 1}