Elliptic curve data - 1225.f1

Formats: - HTML - YAML - JSON - 2025-09-10T21:47:17.542965

• 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': '1225e', 'Clabel': '1225e2', 'Cnumber': 2, 'abc_quality': 1.0734398000116747, 'absD': 11259376953125, 'adelic_genus': 97, 'adelic_index': 2736, 'adelic_level': 5180, 'ainvs': [1, 1, 0, -254901700, 1566310159625], 'analytic_rank': 0, 'bad_primes': [5, 7], 'class_deg': 37, 'class_size': 2, 'cm': 0, 'conductor': 1225, 'degree': 62160, 'elladic_images': ['37.114.4.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0481587592520753028536903072', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 37, 'iso_nlabel': 5, 'isogeny_degrees': [1, 37], 'jinv': [-162677523113838677, 1], 'lmfdb_iso': '1225.f', 'lmfdb_label': '1225.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -208083, -36621194], 'min_quad_twist_disc': -35, 'modell_images': ['37B.8.2'], 'modm_images': ['20.2.0.a.1', '37.114.4.b.2', '148.228.10.?', '185.456.10.?', '259.342.16.?', '740.912.25.?', '1036.684.40.?', '1295.1368.40.?', '5180.2736.97.?'], 'nonmax_primes': [37], 'nonmax_rad': 37, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 245], [5, 14, 49], [7, 26, 25]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54380689222295781849955231165', 'prec': 103}, 'szpiro_ratio': 9.799711230731145, '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.f', 'trace_hash': 1116119215798169805}
• 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': '0.0022511422644390897412509860920', 'prec': 110}, 'conductor': 1225, 'gens': [], 'heights': [], 'lmfdb_label': '1225.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23831784419393556967669239684', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4299070651636134180601543810677786671', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [2, 0], '5': 'a', '7': 'a', '11': [0, 0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '1225.f1'}
• ec_torsion_growth •

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

  
  
  • id: 60881
    {'degree': 3, 'field': [-13, 5, -1, 1], 'lmfdb_label': '1225.f1', 'torsion': [2]}
  • id: 60882
    {'degree': 6, 'field': [20, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '1225.f1', 'torsion': [2, 2]}
  • id: 60883
    {'degree': 8, 'field': [-49, 49, -28, -43, 25, -7, 7, -4, 1], 'lmfdb_label': '1225.f1', 'torsion': [3]}
  • id: 60884
    {'degree': 12, 'field': [20, 145, -155, 375, -229, 33, -15, -7, 29, 7, -5, -3, 1], 'lmfdb_label': '1225.f1', '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: 18071
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1225.f1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 18072
    {'conductor': 1225, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1225.f1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1672280
    {'adelic_gens': [[1, 0, 148, 1], [1, 3256, 0, 1], [5075, 2146, 5143, 4397], [5095, 2072, 5032, 1971], [1, 28, 0, 1], [1037, 0, 0, 2073], [1925, 3256, 1924, 1925], [4441, 0, 0, 3701], [113, 4144, 148, 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.f1', 'prime': 0}
  • id: 5872
    {'conductor': 1225, 'elladic_image': '37.114.4.2', 'lmfdb_label': '1225.f1', 'modell_image': '37B.8.2', 'prime': 37}
• lmfdb_iso 1225.f does not appear in ec_padic