Elliptic curve data - 1800.m4

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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': '1800s', 'Clabel': '1800s2', 'Cnumber': 2, 'abc_quality': 0.972547111469975, 'absD': 26244000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 120, 'ainvs': [0, 0, 0, -975, -8750], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1800, 'degree': 1024, 'elladic_images': ['8.48.0.138'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.70867281447124776033899160825', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [35152, 9], 'lmfdb_iso': '1800.m', 'lmfdb_label': '1800.m4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4, 4], 'min_quad_twist_disc': -15, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.1', '12.24.0.c.1', '20.24.0-4.b.1.2', '24.96.1.bu.1', '40.96.0-8.h.1.7', '60.48.0-12.c.1.2', '120.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.83296517386586589499241664366', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 8, 200], [5, 14, 72]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1074504064531541456038320911', 'prec': 103}, 'szpiro_ratio': 4.304013730726897, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, 0, 0, -4, 2, 2, -4, -8, -6, 8, -6, 6, -4, 0, -2, -4, -2, 4, -8, -10, -8, -4, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 1800, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1800.m', 'trace_hash': 216699688454642961}
• 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': '0.24235646786209592537083288895', 'prec': 103}, 'conductor': 1800, 'gens': [[-19, 54, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.83296517386586589499241664366', 'prec': 103}], 'lmfdb_label': '1800.m4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.87051774000699046838009919079', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9004438426329738350460360566090434854', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-10, 0, 1], [35, 0, 1]], 'xcoord_integral_points': [-25, -19, -15, -10, 35, 39, 65, 125, 710]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [3, 0], '17': [5, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1800.m4'}
• ec_torsion_growth •

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

  
  
  • id: 91810
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 4]}
  • id: 91811
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 4]}
  • id: 91812
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 4]}
  • id: 91817
    {'degree': 8, 'field': [-19, -78, -62, -58, -12, -8, 2, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 6]}
  • id: 91813
    {'degree': 8, 'field': [1, 0, -3, 0, 8, 0, -3, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [4, 4]}
  • id: 91816
    {'degree': 8, 'field': [1, 2, -4, 8, -5, -8, -4, -2, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 8]}
  • id: 91815
    {'degree': 8, 'field': [36, 0, -12, 0, 13, 0, 8, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 8]}
  • id: 91814
    {'degree': 8, 'field': [256, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 8]}
  • id: 91819
    {'degree': 16, 'field': [1, -2, 2, -4, -22, 2, 48, 114, 163, 114, 48, 2, -22, -4, 2, -2, 1], 'lmfdb_label': '1800.m4', 'torsion': [4, 8]}
  • id: 91820
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '1800.m4', 'torsion': [4, 8]}
  • id: 91821
    {'degree': 16, 'field': [186, -252, 1414, -766, 2608, -1936, 1960, -1480, 915, -804, 762, -454, 202, -64, 16, -4, 1], 'lmfdb_label': '1800.m4', 'torsion': [2, 12]}
  • id: 91818
    {'degree': 16, 'field': [441, 0, 1548, 0, -534, 0, -3408, 0, 3715, 0, -1552, 0, 306, 0, -28, 0, 1], 'lmfdb_label': '1800.m4', '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: 29119
    {'conductor': 1800, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '1800.m4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 29120
    {'conductor': 1800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1800.m4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 29121
    {'conductor': 1800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1800.m4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1675806
    {'adelic_gens': [[49, 70, 90, 29], [113, 8, 112, 9], [41, 0, 40, 101], [101, 80, 70, 51], [1, 0, 8, 1], [5, 4, 116, 117], [23, 0, 0, 119], [1, 8, 0, 1]], 'adelic_image': '120.192.1.?', 'conductor': 1800, 'lmfdb_label': '1800.m4', 'prime': 0}
  • id: 8867
    {'conductor': 1800, 'elladic_image': '8.48.0.138', 'lmfdb_label': '1800.m4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 50875
    {'lmfdb_iso': '1800.m', 'p': 11, 'prec': 20, 'unit': 54280183652642930430, 'val': 1}
  • id: 50873
    {'lmfdb_iso': '1800.m', 'p': 13, 'prec': 20, 'unit': 34448735939457962602, 'val': 2}
  • id: 50876
    {'lmfdb_iso': '1800.m', 'p': 17, 'prec': 20, 'unit': 7224044256974685893137, 'val': 2}
  • id: 50877
    {'lmfdb_iso': '1800.m', 'p': 19, 'prec': 20, 'unit': 1243422416316676247192464, 'val': 1}
  • id: 50880
    {'lmfdb_iso': '1800.m', 'p': 23, 'prec': 20, 'unit': 9852627562803717805954563, 'val': 1}
  • id: 50872
    {'lmfdb_iso': '1800.m', 'p': 29, 'prec': 20, 'unit': 971247006486062467793992232, 'val': 1}
  • id: 50884
    {'lmfdb_iso': '1800.m', 'p': 31, 'prec': 20, 'unit': 18622695228612875417649108682, 'val': 1}
  • id: 50868
    {'lmfdb_iso': '1800.m', 'p': 37, 'prec': 20, 'unit': 404622220639306281707719178273, 'val': 1}
  • id: 50870
    {'lmfdb_iso': '1800.m', 'p': 41, 'prec': 20, 'unit': 3497105723278972485710686066059, 'val': 1}
  • id: 50871
    {'lmfdb_iso': '1800.m', 'p': 43, 'prec': 20, 'unit': 3842441173504893300600445551265, 'val': 1}
  • id: 50878
    {'lmfdb_iso': '1800.m', 'p': 53, 'prec': 20, 'unit': 144218843844782008028221323655135, 'val': 1}
  • id: 50882
    {'lmfdb_iso': '1800.m', 'p': 59, 'prec': 20, 'unit': 127852474492494515328474826579643, 'val': 1}
  • id: 50883
    {'lmfdb_iso': '1800.m', 'p': 61, 'prec': 20, 'unit': 436792686467856558642517533926635, 'val': 1}
  • id: 50867
    {'lmfdb_iso': '1800.m', 'p': 67, 'prec': 20, 'unit': 23170175726077659137367297654272051, 'val': 1}
  • id: 50869
    {'lmfdb_iso': '1800.m', 'p': 71, 'prec': 20, 'unit': 81055537268904916652784018087310818, 'val': 1}
  • id: 50879
    {'lmfdb_iso': '1800.m', 'p': 73, 'prec': 20, 'unit': 207824297060111615914786666985263899, 'val': 1}
  • id: 50874
    {'lmfdb_iso': '1800.m', 'p': 79, 'prec': 20, 'unit': 488869849781955752557505528862449645, 'val': 1}
  • id: 50866
    {'lmfdb_iso': '1800.m', 'p': 83, 'prec': 20, 'unit': 603101367635668185929935807093021692, 'val': 1}
  • id: 50881
    {'lmfdb_iso': '1800.m', 'p': 89, 'prec': 20, 'unit': 5980027307334527102728437372774714353, 'val': 1}
  • id: 50865
    {'lmfdb_iso': '1800.m', 'p': 97, 'prec': 20, 'unit': 46936363892402754871544312117931593235, 'val': 1}