Elliptic curve data - 4550.r1

Formats: - HTML - YAML - JSON - 2026-02-02T10:44:50.660375

• 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': '4550p', 'Clabel': '4550p3', 'Cnumber': 3, 'abc_quality': 1.0476037319513174, 'absD': 16065240590756033331200000000, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 32760, 'ainvs': [1, 1, 1, -1262579938, -18313477533969], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 4550, 'degree': 4572288, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.1618667336888665824489290099', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3, 9], 'jinv': [-14245586655234650511684983641, 1028175397808386133196800], 'lmfdb_iso': '4550.r', 'lmfdb_label': '4550.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -50503198, -146507820272], 'min_quad_twist_disc': 5, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '15.8.0-3.a.1.1', '45.24.0-9.a.1.2', '117.36.0.?', '585.72.0.?', '728.2.0.?', '2184.8.0.?', '6552.72.3.?', '10920.16.0.?', '32760.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2275], [3, 2, 325], [5, 18, 182], [7, 8, 325], [13, 14, 350]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.3571477774718163951485493433', 'prec': 100}, 'szpiro_ratio': 8.856873492265683, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 1, 0, -1, -1, 1, -2, 0, -3, -1, -1, -1, 0, 1, -6, -2, 2, 0], 'aplist': [1, -1, 0, -1, -3, -1, -6, 2, -9, 6, 5, 7, 9, 10, -3, 0, 12, -1, 13, -12, -11, 17, 6, -6, 19], 'class_deg': 9, 'class_size': 3, 'conductor': 4550, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '4550.r', 'trace_hash': 105014789268425451}
• 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': '0.00024268810261678222959775597891', 'prec': 113}, 'conductor': 4550, 'gens': [], 'heights': [], 'lmfdb_label': '4550.r1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.012611147043990680367976301879', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5890045275428257263650140367409569331', 'prec': 130}, 'tamagawa_product': 126, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 2], '5': 'a', '7': [2, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '4550.r1'}
• ec_torsion_growth •

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

  
  
  • id: 236456
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4550.r1', 'torsion': [3]}
  • id: 236457
    {'degree': 3, 'field': [-2, 6, -1, 1], 'lmfdb_label': '4550.r1', 'torsion': [2]}
  • id: 236459
    {'degree': 6, 'field': [-845, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '4550.r1', 'torsion': [3]}
  • id: 236461
    {'degree': 6, 'field': [16, -26, 78, -15, 23, -1, 1], 'lmfdb_label': '4550.r1', 'torsion': [6]}
  • id: 236458
    {'degree': 6, 'field': [728, -728, 218, 12, -11, -2, 1], 'lmfdb_label': '4550.r1', 'torsion': [2, 2]}
  • id: 236460
    {'degree': 6, 'field': [6616, 1044, 1542, 79, -63, -3, 1], 'lmfdb_label': '4550.r1', 'torsion': [9]}
  • id: 236462
    {'degree': 12, 'field': [-14447516, -4331544, -156526, -221280, 223460, 48932, 11327, 1844, -531, 124, 13, -4, 1], 'lmfdb_label': '4550.r1', 'torsion': [4]}
  • id: 236463
    {'degree': 12, 'field': [1156, -782, -321, -235, 340, 3, -101, 102, -15, -5, 4, -3, 1], 'lmfdb_label': '4550.r1', 'torsion': [3, 3]}
  • id: 236464
    {'degree': 12, 'field': [124336, 63768, -11496, 5150, -1185, -2817, 1379, -228, -120, 10, 9, -3, 1], 'lmfdb_label': '4550.r1', 'torsion': [9]}
  • id: 236465
    {'degree': 12, 'field': [1134064, 1986064, 1319244, 335984, -39080, -44936, -9327, 358, 515, 12, -1, -2, 1], 'lmfdb_label': '4550.r1', 'torsion': [2, 6]}
  • id: 236466
    {'degree': 18, 'field': [-822438436, -411446862, 571988487, 176313868, -136221465, 3418698, -3981459, 2566884, -493674, -458960, 145482, -11796, 6826, -3006, 975, -212, 51, -6, 1], 'lmfdb_label': '4550.r1', 'torsion': [6]}
  • id: 236467
    {'degree': 18, 'field': [295894134784, 784343247168, 1008285134064, 444990102568, 173935874304, 3379998660, -10571055016, -1740152202, -71497608, 62944671, 19815195, -752394, -717798, -5808, 13836, 284, -162, -3, 1], 'lmfdb_label': '4550.r1', 'torsion': [18]}
• 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: 86389
    {'conductor': 4550, 'conductor_valuation': 1, 'discriminant_valuation': 63, 'j_denominator_valuation': 63, 'kodaira_symbol': 67, 'lmfdb_label': '4550.r1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 63}
  • id: 86390
    {'conductor': 4550, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '4550.r1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 86391
    {'conductor': 4550, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4550.r1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 86392
    {'conductor': 4550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4550.r1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1693514
    {'adelic_gens': [[1, 18, 0, 1], [32743, 18, 32742, 19], [1, 18, 10, 181], [10, 9, 81, 73], [20671, 6570, 22545, 25861], [13103, 0, 0, 32759], [8191, 6570, 0, 1], [1, 0, 18, 1], [24571, 22950, 0, 17291], [18721, 6570, 24345, 26371], [16381, 6570, 3285, 26371]], 'adelic_image': '32760.144.3.?', 'conductor': 4550, 'lmfdb_label': '4550.r1', 'prime': 0}
  • id: 22521
    {'conductor': 4550, 'elladic_image': '9.12.0.1', 'lmfdb_label': '4550.r1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 4550.r does not appear in ec_padic