Elliptic curve data - 61050.x1

Formats: - HTML - YAML - JSON - 2025-10-31T14:33:14.968323

• 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': '61050bd', 'Clabel': '61050bd1', 'Cnumber': 1, 'abc_quality': 0.935660829246625, 'absD': 54327941894531250, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 48840, 'ainvs': [1, 0, 1, -312001, -66160102], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 37], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 61050, 'degree': 1161216, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0107194305490092140382902860', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1], 'jinv': [214965934543825921, 3476988281250], 'lmfdb_iso': '61050.x', 'lmfdb_label': '61050.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -12480, -534273], 'min_quad_twist_disc': 5, 'modell_images': [], 'modm_images': ['48840.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 30525], [3, 4, 20350], [5, 18, 2442], [7, 2, 20350], [11, 12, 5550], [37, 38, 1650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2060004743319590267379106194', 'prec': 100}, 'szpiro_ratio': 4.498036678799504, '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, -3, -1, 1, 0, 1, 1, 1, 3, 0, 1, 7, -1, 8, 0], 'aplist': [-1, 1, 0, -3, 1, 1, 7, 8, -6, 5, 4, 1, 7, -1, 11, 14, 12, -10, -7, 10, 14, 4, -7, 11, -1], 'class_deg': 1, 'class_size': 1, 'conductor': 61050, 'isogeny_matrix': [[1]], 'lmfdb_iso': '61050.x', 'trace_hash': 1629600242124061729}
• 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': '0.017927151691949653116773011437', 'prec': 107}, 'conductor': 61050, 'gens': [], 'heights': [], 'lmfdb_label': '61050.x1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20220252765714752903027419005', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8308353872000654064238386606793809603', 'prec': 130}, 'tamagawa_product': 14, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [13, 0], '3': [1, 0], '5': 'a', '7': [2, 0], '11': [1, 0], '13': [2, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [1, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '61050.x1'}
• ec_torsion_growth •

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

  
  
  • id: 2926474
    {'degree': 3, 'field': [-120, -56, -1, 1], 'lmfdb_label': '61050.x1', 'torsion': [2]}
  • id: 2926475
    {'degree': 6, 'field': [1776, 5328, 2134, -656, -231, -2, 1], 'lmfdb_label': '61050.x1', 'torsion': [2, 2]}
  • id: 2926476
    {'degree': 8, 'field': [-386354, 62789, -64898, 4217, -2105, -7, 7, -4, 1], 'lmfdb_label': '61050.x1', 'torsion': [3]}
  • id: 2926477
    {'degree': 12, 'field': [6998702626, 2214296204, -250345891, -263228340, -114627305, -18720056, 2116831, 478456, -14105, -1560, -91, -4, 1], 'lmfdb_label': '61050.x1', '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: 1470559
    {'conductor': 61050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '61050.x1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1470560
    {'conductor': 61050, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '61050.x1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1470561
    {'conductor': 61050, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '61050.x1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1470562
    {'conductor': 61050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '61050.x1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1470563
    {'conductor': 61050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '61050.x1', 'prime': 37, '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': [[35521, 2, 35521, 3], [32561, 2, 32561, 3], [48839, 2, 48838, 3], [19537, 2, 19537, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 48839, 0], [3961, 2, 3961, 3], [24421, 2, 24421, 3], [36631, 2, 0, 1]], 'adelic_image': '48840.2.0.?', 'conductor': 61050, 'lmfdb_label': '61050.x1', 'prime': 0}
• lmfdb_iso 61050.x does not appear in ec_padic