Elliptic curve data - 3900.b2

Formats: - HTML - YAML - JSON - 2025-09-12T18:13:39.339528

• 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': '3900b', 'Clabel': '3900b2', 'Cnumber': 2, 'abc_quality': 1.0339743089656475, 'absD': 5497372474963200, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 780, 'ainvs': [0, -1, 0, 14572, -3507288], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 3900, 'degree': 15552, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7008252356217104857385178498', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [53465227872560, 858964449213], 'lmfdb_iso': '3900.b', 'lmfdb_label': '3900.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 14572, -3507288], 'min_quad_twist_disc': 1, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '15.8.0-3.a.1.1', '52.2.0.a.1', '156.8.0.?', '780.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 325], [3, 4, 100], [5, 10, 156], [13, 14, 300]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.97048746317606355036023654662', 'prec': 103}, 'szpiro_ratio': 5.280263284575623, '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, 0, 0, 1, 0, 1, 0, -3, 0, -1, 0, 0, 0, -3, 0, -4, 0], 'aplist': [0, -1, 0, 1, -3, -1, -3, -4, 6, 3, -1, -2, 0, 10, 3, 3, 3, 5, 7, 0, -2, -10, 15, 0, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 3900, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '3900.b', 'trace_hash': 2076996667698563864}
• 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': '0.033318233768277267091239889074', 'prec': 107}, 'conductor': 3900, 'gens': [], 'heights': [], 'lmfdb_label': '3900.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20918029381477291292494444646', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2550817628886374775496666787381544309', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 1], '5': 'a', '7': [2, 0], '11': [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, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '3900.b2'}
• ec_torsion_growth •

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

  
  
  • id: 203050
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '3900.b2', 'torsion': [3]}
  • id: 203051
    {'degree': 3, 'field': [-13, -3, -1, 1], 'lmfdb_label': '3900.b2', 'torsion': [2]}
  • id: 203053
    {'degree': 6, 'field': [-720, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3900.b2', 'torsion': [3]}
  • id: 203052
    {'degree': 6, 'field': [36, 48, 41, 22, 6, -2, 1], 'lmfdb_label': '3900.b2', 'torsion': [2, 2]}
  • id: 203054
    {'degree': 6, 'field': [114, -162, 55, 20, -10, -2, 1], 'lmfdb_label': '3900.b2', 'torsion': [6]}
  • id: 203055
    {'degree': 12, 'field': [81, -1134, 1044, -8070, 5645, -2264, 396, 224, -35, 10, 4, -6, 1], 'lmfdb_label': '3900.b2', 'torsion': [4]}
  • id: 203057
    {'degree': 12, 'field': [21904, 0, -11488, 0, 2040, 0, 400, 0, -135, 0, 2, 0, 1], 'lmfdb_label': '3900.b2', 'torsion': [2, 6]}
  • id: 203056
    {'degree': 12, 'field': [95401, 71733, -6381, -560, -1155, -1707, 1424, -273, -75, -10, 9, -3, 1], 'lmfdb_label': '3900.b2', 'torsion': [3, 3]}
  • id: 203058
    {'degree': 18, 'field': [8136, 14688, 16200, -4536, 11340, -4212, 21474, -15930, -4698, 2415, 225, 135, 430, -120, -45, -1, -3, 0, 1], 'lmfdb_label': '3900.b2', 'torsion': [9]}
  • id: 203059
    {'degree': 18, 'field': [46656, 0, 0, -614304, 0, 0, 208980, 0, 0, -29160, 0, 0, 2160, 0, 0, -84, 0, 0, 1], 'lmfdb_label': '3900.b2', 'torsion': [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: 72501
    {'conductor': 3900, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '3900.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 72502
    {'conductor': 3900, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3900.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 72503
    {'conductor': 3900, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '3900.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 72504
    {'conductor': 3900, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '3900.b2', '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

  
  
  • id: 1689311
    {'adelic_gens': [[4, 3, 9, 7], [775, 6, 774, 7], [458, 327, 595, 7], [301, 6, 123, 19], [471, 2, 10, 7], [391, 6, 393, 19], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '780.16.0.?', 'conductor': 3900, 'lmfdb_label': '3900.b2', 'prime': 0}
  • id: 19370
    {'conductor': 3900, 'elladic_image': '3.4.0.1', 'lmfdb_label': '3900.b2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 3900.b does not appear in ec_padic