Elliptic curve data - 1725.e2

Formats: - HTML - YAML - JSON - 2025-12-22T04:23:15.576258

• 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': '1725f', 'Clabel': '1725f1', 'Cnumber': 1, 'abc_quality': 0.9906117492663808, 'absD': 3234375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [1, 1, 1, -13, -94], 'analytic_rank': 0, 'bad_primes': [3, 5, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1725, 'degree': 288, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.069248182334591561329250849810', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [-15625, 207], 'lmfdb_iso': '1725.e', 'lmfdb_label': '1725.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1, -1], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '46.6.0.a.1', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 575], [3, 4, 575], [5, 14, 69], [23, 24, 75]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87396713855164174862963051642', 'prec': 107}, 'szpiro_ratio': 3.0171574812469175, '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, -1, -1, -1, 0, 1, 2, 3, 1, 0, 4, 1, 6, -2, 0, -1, -4, -1, 2, 0], 'aplist': [-1, -1, 0, 2, 4, 6, -4, 2, 1, 2, 4, -2, 2, -10, 0, 12, -12, -6, 10, 8, 14, 10, -12, -16, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 1725, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1725.e', 'trace_hash': 2124748407532706974}
• 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': '1.1485455062197159608261147196', 'prec': 100}, 'conductor': 1725, 'gens': [], 'heights': [], 'lmfdb_label': '1725.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0759350304953846027703642208', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0759350304953846027703642207579737359', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[5, -3, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 0], '5': 'a', '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1725.e2'}
• ec_torsion_growth •

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

  
  
  • id: 87489
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '1725.e2', 'torsion': [2, 2]}
  • id: 87490
    {'degree': 4, 'field': [-26, -30, 11, 0, 1], 'lmfdb_label': '1725.e2', 'torsion': [4]}
  • id: 87492
    {'degree': 8, 'field': [576, 0, -684, 0, 172, 0, 29, 0, 1], 'lmfdb_label': '1725.e2', 'torsion': [2, 4]}
  • id: 87491
    {'degree': 8, 'field': [1296, 0, -36, 0, 216, 0, -1, 0, 1], 'lmfdb_label': '1725.e2', 'torsion': [2, 4]}
  • id: 87493
    {'degree': 8, 'field': [1475, -505, -1099, -25, 143, 32, 1, -2, 1], 'lmfdb_label': '1725.e2', 'torsion': [6]}
  • id: 87494
    {'degree': 16, 'field': [9801, 0, 412452, 0, -304938, 0, 94068, 0, -10557, 0, 1908, 0, 282, 0, -48, 0, 1], 'lmfdb_label': '1725.e2', 'torsion': [8]}
  • id: 87495
    {'degree': 16, 'field': [23634249, 13033020, 22565011, -8628608, 1191700, -1629049, 335159, -29254, 75827, -13549, 4217, -1813, 365, -55, 22, -2, 1], 'lmfdb_label': '1725.e2', 'torsion': [2, 6]}
• 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: 27570
    {'conductor': 1725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1725.e2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 27571
    {'conductor': 1725, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1725.e2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 27572
    {'conductor': 1725, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1725.e2', 'prime': 23, '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

  
  
  • id: 1675317
    {'adelic_gens': [[1, 0, 4, 1], [185, 4, 94, 9], [3, 4, 8, 11], [1, 2, 2, 5], [194, 1, 179, 0], [1, 4, 0, 1], [273, 4, 272, 5], [73, 208, 68, 207]], 'adelic_image': '276.12.0.?', 'conductor': 1725, 'lmfdb_label': '1725.e2', 'prime': 0}
  • id: 8469
    {'conductor': 1725, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1725.e2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1725.e does not appear in ec_padic