Elliptic curve data - 187200.o1

Formats: - HTML - YAML - JSON - 2025-12-29T21:58:10.359200

• 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': '187200ck', 'Clabel': '187200ck4', 'Cnumber': 4, 'abc_quality': 0.9373389475551026, 'absD': 1599050419200000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -1490700, -697894000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 4718592, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3459189160431051813882390539', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4], 'jinv': [490757540836, 2142075], 'lmfdb_iso': '187200.o', 'lmfdb_label': '187200.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1656, -26400], 'min_quad_twist_disc': 120, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0.h.1', '40.12.0-4.c.1.1', '104.12.0.?', '120.24.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 8, 20800], [5, 18, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.067697574745406402500593940216', 'prec': 107}, 'szpiro_ratio': 4.469371687065822, '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, 0, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, -6, 0, 0, 0], 'aplist': [0, 0, 0, -4, -4, 1, -6, 0, 8, 6, 4, -2, 10, 4, 8, 2, -12, 2, 16, -8, 6, 16, 4, 2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 187200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '187200.o', 'trace_hash': 1501977996438861781}
• 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': '0.0091698180747593101888155101707', 'prec': 110}, 'conductor': 187200, 'gens': [], 'heights': [], 'lmfdb_label': '187200.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13666775006201076501670333390', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1866840009921722402672533424457880947', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-740, 0, 1]], 'xcoord_integral_points': [-740]}
• lmfdb_label 187200.o1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8249829
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 2]}
  • id: 8249830
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [4]}
  • id: 8249831
    {'degree': 2, 'field': [30, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [4]}
  • id: 8249832
    {'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 4]}
  • id: 8249836
    {'degree': 8, 'field': [-410700, 0, -149160, 0, 9000, 0, -170, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [6]}
  • id: 8249833
    {'degree': 8, 'field': [4, 0, -88, 0, 60, 0, -16, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 4]}
  • id: 8249834
    {'degree': 8, 'field': [1600, 0, -470, 0, 81, 0, -2, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [8]}
  • id: 8249835
    {'degree': 8, 'field': [50625, 0, 7500, 0, 475, 0, -10, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [8]}
  • id: 8249837
    {'degree': 16, 'field': [16, 0, -352, 0, 7504, 0, -5152, 0, 2188, 0, -784, 0, 196, 0, -16, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [4, 4]}
  • id: 8249838
    {'degree': 16, 'field': [440896, 0, -626944, 0, 357556, 0, -110764, 0, 25009, 0, -4216, 0, 238, 0, 20, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 8]}
  • id: 8249839
    {'degree': 16, 'field': [2692881, 2973492, -1620162, -2336328, 310978, 843468, 6642, -206188, 3359, 28400, -2050, -1876, 252, 0, 20, -8, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 8]}
  • id: 8249840
    {'degree': 16, 'field': [3515625, 0, -300000, 0, 3939100, 0, -24000, 0, -341250, 0, 2080, 0, -2100, 0, 0, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [2, 6]}
  • id: 8249841
    {'degree': 16, 'field': [141610000, 0, -82312000, 0, 2677600, 0, 2654000, 0, 160600, 0, 4520, 0, -500, 0, 20, 0, 1], 'lmfdb_label': '187200.o1', 'torsion': [12]}
  • id: 8249842
    {'degree': 16, 'field': [693005625, 0, 184801500, 0, 12320100, 0, 16402500, 0, 935550, 0, 34020, 0, 900, 0, 60, 0, 1], 'lmfdb_label': '187200.o1', '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: 4631212
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '187200.o1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4631213
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '187200.o1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4631214
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '187200.o1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4631215
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '187200.o1', 'prime': 13, 'reduction_type': 1, '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: 2866830
    {'adelic_gens': [[269, 270, 1430, 29], [1, 0, 8, 1], [824, 1245, 515, 934], [1, 8, 0, 1], [1, 4, 4, 17], [504, 655, 1415, 744], [623, 0, 0, 1559], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1081, 320, 580, 1281]], 'adelic_image': '1560.48.0.?', 'conductor': 187200, 'lmfdb_label': '187200.o1', 'prime': 0}
  • id: 699496
    {'conductor': 187200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '187200.o1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187200.o does not appear in ec_padic