Elliptic curve data - 20475.s1

Formats: - HTML - YAML - JSON - 2025-10-25T04:12:48.866712

• 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': '20475bd', 'Clabel': '20475bd2', 'Cnumber': 2, 'abc_quality': 0.9360324336468434, 'absD': 48107824857421875, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1820, 'ainvs': [1, -1, 0, -93492, -3091959], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 20475, 'degree': 161280, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8923893390878723268539512533', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [63473450669, 33787663], 'lmfdb_iso': '20475.s', 'lmfdb_label': '20475.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -415, 750], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '140.6.0.?', '260.6.0.?', '364.6.0.?', '1820.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.5040791708836755568235080985', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 315], [3, 6, 175], [5, 14, 819], [7, 8, 2925], [13, 14, 1575]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.13600476042824220020575913492', 'prec': 103}, 'szpiro_ratio': 4.628859481870401, '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, 0, -1, 0, 0, -1, -3, 0, 0, -6, 0, -1, -1, 0, -1, 2, 0, 0, 0], 'aplist': [1, 0, 0, -1, -6, -1, 2, 0, 0, 2, 8, 2, 4, -4, 12, 0, -4, -14, -4, 2, -6, 16, 4, 0, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 20475, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '20475.s', 'trace_hash': 1580031036820368186}
• 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': '0.022713889299886963780279294696', 'prec': 107}, 'conductor': 20475, 'gens': [[-875, 88919, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '8.5040791708836755568235080985', 'prec': 100}], 'lmfdb_label': '20475.s1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.29010592755371774867129892868', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9341675517189193592074404567586854737', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-1149, 1149, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '20475.s1'}
• ec_torsion_growth •

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

  
  
  • id: 1046181
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '20475.s1', 'torsion': [2, 2]}
  • id: 1046182
    {'degree': 4, 'field': [166, 19, 11, -1, 1], 'lmfdb_label': '20475.s1', 'torsion': [4]}
  • id: 1046185
    {'degree': 8, 'field': [-9, -28, -44, -24, -11, -7, -6, -1, 1], 'lmfdb_label': '20475.s1', 'torsion': [6]}
  • id: 1046183
    {'degree': 8, 'field': [261121, 0, -68012, 0, -4501, 0, -28, 0, 1], 'lmfdb_label': '20475.s1', 'torsion': [2, 4]}
  • id: 1046184
    {'degree': 8, 'field': [828100, 0, -72800, 0, 1845, 0, 10, 0, 1], 'lmfdb_label': '20475.s1', 'torsion': [2, 4]}
  • id: 1046187
    {'degree': 16, 'field': [10871501, 9366952, -49377, -172258, 1773141, 1560060, 370062, -107450, -34278, 670, -2043, -1230, 21, 68, 3, -2, 1], 'lmfdb_label': '20475.s1', 'torsion': [2, 6]}
  • id: 1046186
    {'degree': 16, 'field': [102600002911, -131075977042, 84069008590, -33923017450, 8756713849, -1227050542, -36094372, 57164080, -11446134, 609818, 173138, -32146, 389, 566, -36, -4, 1], 'lmfdb_label': '20475.s1', 'torsion': [8]}
• 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: 465385
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '20475.s1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 465386
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '20475.s1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 465387
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '20475.s1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 465388
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '20475.s1', 'prime': 13, 'reduction_type': -1, '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: 1800999
    {'adelic_gens': [[1042, 1, 1299, 0], [561, 4, 1122, 9], [1, 2, 2, 5], [1, 4, 0, 1], [456, 1369, 1365, 456], [368, 1, 363, 0], [1, 0, 4, 1], [1817, 4, 1816, 5], [3, 4, 8, 11]], 'adelic_image': '1820.12.0.?', 'conductor': 20475, 'lmfdb_label': '20475.s1', 'prime': 0}
  • id: 95422
    {'conductor': 20475, 'elladic_image': '2.3.0.1', 'lmfdb_label': '20475.s1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 953459
    {'lmfdb_iso': '20475.s', 'p': 11, 'prec': 20, 'unit': 16589907954429431091, 'val': 1}
  • id: 953466
    {'lmfdb_iso': '20475.s', 'p': 17, 'prec': 20, 'unit': 118840399487617490372233, 'val': 1}
  • id: 953464
    {'lmfdb_iso': '20475.s', 'p': 29, 'prec': 20, 'unit': 5104404466380846865476032286, 'val': 1}
  • id: 953472
    {'lmfdb_iso': '20475.s', 'p': 31, 'prec': 20, 'unit': 8893799589366082374630601355, 'val': 1}
  • id: 953460
    {'lmfdb_iso': '20475.s', 'p': 37, 'prec': 20, 'unit': 114178106497604109430593409616, 'val': 1}
  • id: 953462
    {'lmfdb_iso': '20475.s', 'p': 41, 'prec': 20, 'unit': 2795169492747158652362423793609, 'val': 1}
  • id: 953463
    {'lmfdb_iso': '20475.s', 'p': 43, 'prec': 20, 'unit': 9004854102527217189577812166371, 'val': 1}
  • id: 953470
    {'lmfdb_iso': '20475.s', 'p': 47, 'prec': 20, 'unit': 7502836640327697439377079723325, 'val': 1}
  • id: 953468
    {'lmfdb_iso': '20475.s', 'p': 59, 'prec': 20, 'unit': 1485683586617644811131472053192818, 'val': 1}
  • id: 953471
    {'lmfdb_iso': '20475.s', 'p': 61, 'prec': 20, 'unit': 7443313483580118546278398816655509, 'val': 1}
  • id: 953458
    {'lmfdb_iso': '20475.s', 'p': 67, 'prec': 20, 'unit': 13283270469583597947265903326959916, 'val': 1}
  • id: 953461
    {'lmfdb_iso': '20475.s', 'p': 71, 'prec': 20, 'unit': 92376857332415687243182688424224250, 'val': 1}
  • id: 953469
    {'lmfdb_iso': '20475.s', 'p': 73, 'prec': 20, 'unit': 104319568285641524984204193525348942, 'val': 1}
  • id: 953465
    {'lmfdb_iso': '20475.s', 'p': 79, 'prec': 20, 'unit': 242180287021432182803816646986500114, 'val': 1}
  • id: 953467
    {'lmfdb_iso': '20475.s', 'p': 83, 'prec': 20, 'unit': 1451173716456977332825775969118036177, 'val': 1}
  • id: 953457
    {'lmfdb_iso': '20475.s', 'p': 97, 'prec': 20, 'unit': 35491511210111618664599829325083891141, 'val': 1}