Elliptic curve data - 38720.bn4

Formats: - HTML - YAML - JSON - 2025-10-20T09:54:14.683848

• 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': '38720g', 'Clabel': '38720g3', 'Cnumber': 3, 'abc_quality': 1.1038914936992343, 'absD': 3429742096000000000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 880, 'ainvs': [0, 0, 0, -1271468, -2871190608], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 38720, 'degree': 2211840, 'elladic_images': ['8.24.0.75'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8136271908440157980293071172', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1957960715364, 29541015625], 'lmfdb_iso': '38720.bn', 'lmfdb_label': '38720.bn4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -2627, 269646], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0-4.d.1.4', '40.48.0-40.w.1.8', '44.24.0.d.1', '80.96.0.?', '88.48.0.?', '440.96.1.?', '880.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 2, 7744], [5, 6, 7744], [11, 72, 320]], 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.69048331369823678010869249961', 'prec': 103}, 'szpiro_ratio': 5.403117012475933, '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, 0, 0, 0, -1, 0, -4, 0, -3, 0, 0, 0, 6, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, -1, -4, 0, 6, 6, 4, 4, -2, 8, 10, -10, 0, 4, 10, 4, -2, 8, 0, 14, 16, -8, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 38720, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '38720.bn', 'trace_hash': 577909436384605693}
• 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': '0.0035984417239460702661125577394', 'prec': 110}, 'conductor': 38720, 'gens': [], 'heights': [], 'lmfdb_label': '38720.bn4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.060395907140646377007252184970', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1742526570632695722610786589178087133', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[1716, 0, 1]], 'xcoord_integral_points': [1716]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 2, 0], '5': [0, 0], '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '38720.bn4'}
• ec_torsion_growth •

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

  
  
  • id: 1908638
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [4]}
  • id: 1908637
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [2, 2]}
  • id: 1908639
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [4]}
  • id: 1908640
    {'degree': 4, 'field': [121, 0, 0, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [2, 4]}
  • id: 1908644
    {'degree': 8, 'field': [-5808, 0, -3168, 0, 264, 0, 0, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [6]}
  • id: 1908641
    {'degree': 8, 'field': [81, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [4, 4]}
  • id: 1908643
    {'degree': 8, 'field': [361, 0, 604, 0, 207, 0, 26, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [8]}
  • id: 1908642
    {'degree': 8, 'field': [14641, 0, -7986, 0, 847, 0, -44, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [8]}
  • id: 1908645
    {'degree': 16, 'field': [3721, 0, 312456, 0, 474346, 0, 300716, 0, 94999, 0, 15724, 0, 1378, 0, 60, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [2, 8]}
  • id: 1908647
    {'degree': 16, 'field': [21250, -20600, 13580, -4536, 23066, -5908, 616, -6420, 2620, 1104, 2062, 256, 194, -60, 8, -4, 1], 'lmfdb_label': '38720.bn4', 'torsion': [2, 6]}
  • id: 1908648
    {'degree': 16, 'field': [45226, -77200, 23064, -9992, -2350, 31620, -23336, 1148, 5442, -5152, 2362, 396, -586, 88, 12, -4, 1], 'lmfdb_label': '38720.bn4', 'torsion': [12]}
  • id: 1908646
    {'degree': 16, 'field': [18241441, 4031824, -2885798, -2255768, 1027002, 152104, -109534, 62756, -27061, 1612, 5094, -2268, -168, 224, -12, -8, 1], 'lmfdb_label': '38720.bn4', 'torsion': [2, 8]}
  • id: 1908649
    {'degree': 16, 'field': [23425600, 0, 4940672, 0, 123904, 0, 27104, 0, 30976, 0, 6776, 0, 748, 0, 44, 0, 1], 'lmfdb_label': '38720.bn4', 'torsion': [12]}
• 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: 913973
    {'conductor': 38720, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '38720.bn4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 913974
    {'conductor': 38720, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '38720.bn4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 913975
    {'conductor': 38720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '38720.bn4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1922293
    {'adelic_gens': [[1, 16, 0, 1], [207, 108, 104, 219], [465, 714, 726, 173], [1, 12, 4, 49], [177, 16, 364, 193], [1, 0, 16, 1], [496, 401, 833, 184], [5, 16, 64, 205], [865, 16, 864, 17]], 'adelic_image': '880.192.3.?', 'conductor': 38720, 'lmfdb_label': '38720.bn4', 'prime': 0}
  • id: 170282
    {'conductor': 38720, 'elladic_image': '8.24.0.75', 'lmfdb_label': '38720.bn4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 38720.bn does not appear in ec_padic