Elliptic curve data - 18720.b4

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• 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': '18720l', 'Clabel': '18720l4', 'Cnumber': 4, 'abc_quality': 1.1541079700404029, 'absD': 9979281000000000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 3120, 'ainvs': [0, 0, 0, 469572, -88096448], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 18720, 'degree': 393216, 'elladic_images': ['4.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3330976668866373228340682148', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [3834800837445824, 3342041015625], 'lmfdb_iso': '18720.b', 'lmfdb_label': '18720.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 52175, -3280223], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '12.24.0-4.d.1.1', '40.24.0.bf.1', '80.48.0.?', '104.24.0.?', '120.48.0.?', '240.96.0.?', '312.48.0.?', '520.48.1.?', '1040.96.3.?', '1560.96.1.?', '3120.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.1539687300807859477810546229', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 416], [5, 6, 3744], [13, 14, 1440]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0906443419926371677192134749', 'prec': 100}, 'szpiro_ratio': 5.163214220426117, '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, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -8, 0], 'aplist': [0, 0, -1, -4, 0, 1, -2, -8, 4, -6, 8, 6, 6, 4, 4, -6, 8, -10, -4, 8, -14, 0, 12, 6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 18720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '18720.b', 'trace_hash': 627769841049341645}
• 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': '0.0094079958045277144335755898624', 'prec': 110}, 'conductor': 18720, 'gens': [[5417, 670293, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '7.1539687300807859477810546229', 'prec': 100}], 'lmfdb_label': '18720.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12620983241312232271398212398', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6116047780488540771663160154043415878', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[176, 0, 1]], 'xcoord_integral_points': [176]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [3, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '18720.b4'}
• ec_torsion_growth •

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

  
  
  • id: 958138
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [4]}
  • id: 958139
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '18720.b4', 'torsion': [4]}
  • id: 958137
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [2, 2]}
  • id: 958140
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [2, 4]}
  • id: 958144
    {'degree': 8, 'field': [-27, 0, -96, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [6]}
  • id: 958143
    {'degree': 8, 'field': [81, 0, 18, 0, 13, 0, -2, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [8]}
  • id: 958142
    {'degree': 8, 'field': [5476, 0, -70464, 0, 5332, 0, 144, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [8]}
  • id: 958141
    {'degree': 8, 'field': [28561, 0, 0, 0, -169, 0, 0, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [4, 4]}
  • id: 958146
    {'degree': 16, 'field': [1, 0, 0, 0, -38, 0, 0, 0, 1443, 0, 0, 0, -38, 0, 0, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [2, 8]}
  • id: 958147
    {'degree': 16, 'field': [65, -624, 2626, -6160, 9322, -9892, 7302, -3292, 323, 832, -646, 220, 24, -56, 28, -8, 1], 'lmfdb_label': '18720.b4', 'torsion': [2, 6]}
  • id: 958148
    {'degree': 16, 'field': [78, -372, 316, 1876, -4004, 124, 5218, -3044, -1365, 1872, -810, 196, 28, -56, 28, -8, 1], 'lmfdb_label': '18720.b4', 'torsion': [12]}
  • id: 958149
    {'degree': 16, 'field': [729, 0, -2592, 0, 8730, 0, -1728, 0, 351, 0, -192, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '18720.b4', 'torsion': [12]}
  • id: 958145
    {'degree': 16, 'field': [78980109156, 8329847760, 11156505048, 687644256, 866058124, 43335856, 44741224, 3050136, 1857162, 135368, 63072, 2848, 2262, -96, 76, -4, 1], 'lmfdb_label': '18720.b4', 'torsion': [2, 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: 421858
    {'conductor': 18720, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '18720.b4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 421859
    {'conductor': 18720, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '18720.b4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 421860
    {'conductor': 18720, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '18720.b4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 421861
    {'conductor': 18720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '18720.b4', '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: 1789036
    {'adelic_gens': [[1039, 0, 0, 3119], [1, 16, 0, 1], [2416, 2811, 915, 616], [1135, 1206, 714, 1987], [1, 12, 4, 49], [1051, 3006, 2802, 2563], [1, 0, 16, 1], [5, 16, 64, 205], [3105, 16, 3104, 17], [2497, 1056, 1668, 1105]], 'adelic_image': '3120.192.3.?', 'conductor': 18720, 'lmfdb_label': '18720.b4', 'prime': 0}
  • id: 87547
    {'conductor': 18720, 'elladic_image': '4.12.0.9', 'lmfdb_label': '18720.b4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 862966
    {'lmfdb_iso': '18720.b', 'p': 7, 'prec': 20, 'unit': 1431785004078823, 'val': 1}
  • id: 862971
    {'lmfdb_iso': '18720.b', 'p': 17, 'prec': 20, 'unit': 45377814386633312000004, 'val': 1}
  • id: 862962
    {'lmfdb_iso': '18720.b', 'p': 19, 'prec': 20, 'unit': 881388261553095032920521, 'val': 1}
  • id: 862975
    {'lmfdb_iso': '18720.b', 'p': 23, 'prec': 20, 'unit': 9492875259417487951863579, 'val': 1}
  • id: 862969
    {'lmfdb_iso': '18720.b', 'p': 29, 'prec': 20, 'unit': 1876590749481338049676590537, 'val': 1}
  • id: 862980
    {'lmfdb_iso': '18720.b', 'p': 31, 'prec': 20, 'unit': 6698671732727516690812678866, 'val': 1}
  • id: 862965
    {'lmfdb_iso': '18720.b', 'p': 37, 'prec': 20, 'unit': 13090531023794070580111842185, 'val': 1}
  • id: 862967
    {'lmfdb_iso': '18720.b', 'p': 41, 'prec': 20, 'unit': 2674975758261203120246245214244, 'val': 1}
  • id: 862968
    {'lmfdb_iso': '18720.b', 'p': 43, 'prec': 20, 'unit': 4901373963933951412544268931260, 'val': 1}
  • id: 862970
    {'lmfdb_iso': '18720.b', 'p': 47, 'prec': 20, 'unit': 1978972716976210216111211843276, 'val': 1}
  • id: 862973
    {'lmfdb_iso': '18720.b', 'p': 53, 'prec': 20, 'unit': 28565905687193066957250242612782, 'val': 1}
  • id: 862978
    {'lmfdb_iso': '18720.b', 'p': 59, 'prec': 20, 'unit': 3185599976615437735598807267901085, 'val': 1}
  • id: 862979
    {'lmfdb_iso': '18720.b', 'p': 61, 'prec': 20, 'unit': 4744005363243091478822378557003613, 'val': 1}
  • id: 862964
    {'lmfdb_iso': '18720.b', 'p': 67, 'prec': 20, 'unit': 16762631937126032056227687230490970, 'val': 1}
  • id: 862977
    {'lmfdb_iso': '18720.b', 'p': 71, 'prec': 20, 'unit': 44766838105157771976371984354196930, 'val': 1}
  • id: 862974
    {'lmfdb_iso': '18720.b', 'p': 73, 'prec': 20, 'unit': 3322891559197188956468211897300706, 'val': 1}
  • id: 862972
    {'lmfdb_iso': '18720.b', 'p': 83, 'prec': 20, 'unit': 391227820996911196524172674203276752, 'val': 1}
  • id: 862976
    {'lmfdb_iso': '18720.b', 'p': 89, 'prec': 20, 'unit': 2990095396663654945625377340457478515, 'val': 1}
  • id: 862963
    {'lmfdb_iso': '18720.b', 'p': 97, 'prec': 20, 'unit': 50164567990396829714540909906548994548, 'val': 1}