Elliptic curve data - 122304.r1

Formats: - HTML - YAML - JSON - 2025-10-29T09:26:46.714052

• 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': '122304bk', 'Clabel': '122304bk1', 'Cnumber': 1, 'abc_quality': 0.964946780244582, 'absD': 5891559969463074816, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2184, 'ainvs': [0, -1, 0, -2021217, 1112853729], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 122304, 'degree': 4055040, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4384348213429251430267498302', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1], 'jinv': [-59219479733906, 382060497], 'lmfdb_iso': '122304.r', 'lmfdb_label': '122304.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -10312, -401876], 'min_quad_twist_disc': -56, 'modell_images': [], 'modm_images': ['2184.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1911], [3, 4, 40768], [5, 2, 9408], [7, 32, 2496], [13, 14, 9408]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.48352124102201263546632795308', 'prec': 103}, 'szpiro_ratio': 4.7106942834087215, '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, -1, 0, -3, 0, 0, 0, 1, 0, 5, 0, -1, 0, 3, 0, -3, 0, -1, 0], 'aplist': [0, -1, -3, 0, 5, -1, -3, -1, 1, 5, 8, -1, 12, -11, -8, -10, -8, 13, -2, 8, -11, 2, -18, -18, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 122304, 'isogeny_matrix': [[1]], 'lmfdb_iso': '122304.r', 'trace_hash': 1946078688457957830}
• 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': '0.0076208326569646851415544402943', 'prec': 110}, 'conductor': 122304, 'gens': [], 'heights': [], 'lmfdb_label': '122304.r1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24084273294715193880128671403', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.96337093178860775520514685613032948974', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': 'a', '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [2, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '122304.r1'}
• ec_torsion_growth •

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

  
  
  • id: 5585171
    {'degree': 3, 'field': [-9, 13, -1, 1], 'lmfdb_label': '122304.r1', 'torsion': [2]}
  • id: 5585172
    {'degree': 6, 'field': [2328, -2136, 574, -20, -3, -2, 1], 'lmfdb_label': '122304.r1', 'torsion': [2, 2]}
  • id: 5585173
    {'degree': 8, 'field': [-11524800, 0, 318304, 0, -11760, 0, 0, 0, 1], 'lmfdb_label': '122304.r1', 'torsion': [3]}
  • id: 5585174
    {'degree': 12, 'field': [-6849024, 0, 749708, 0, 201897, 0, 5620, 0, -118, 0, 0, 0, 1], 'lmfdb_label': '122304.r1', '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: 3011652
    {'conductor': 122304, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '122304.r1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3011653
    {'conductor': 122304, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '122304.r1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3011654
    {'conductor': 122304, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '122304.r1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3011655
    {'conductor': 122304, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '122304.r1', 'prime': 13, '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': [[1457, 2, 1457, 3], [2017, 2, 2017, 3], [1, 0, 2, 1], [1093, 2, 1093, 3], [1, 2, 0, 1], [2183, 2, 2182, 3], [1249, 2, 1249, 3], [1639, 2, 1639, 3], [1, 1, 2183, 0]], 'adelic_image': '2184.2.0.?', 'conductor': 122304, 'lmfdb_label': '122304.r1', 'prime': 0}
• lmfdb_iso 122304.r does not appear in ec_padic