Elliptic curve data - 550.j2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '550k', 'Clabel': '550k1', 'Cnumber': 1, 'abc_quality': 1.0648872065191846, 'absD': 2750, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 2200, 'ainvs': [1, 1, 1, -28, -69], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 550, 'degree': 48, 'elladic_images': ['25.120.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.42630985143223593350414229183', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 5, 25], 'jinv': [-19465109, 22], 'lmfdb_iso': '550.j', 'lmfdb_label': '550.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -28, -69], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '25.120.0-25.a.2.2', '275.600.12.?', '440.48.1.?', '2200.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 55], [11, 12, 50]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.82866932954076102715433212514', 'prec': 107}, 'szpiro_ratio': 3.4254641742336243, '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, 3, 1, -2, 0, 1, -1, 4, 3, 0, 1, 3, -2, -5, 0], 'aplist': [1, -1, 0, 3, 1, 4, 3, -5, 4, 5, 7, -7, -8, -6, 8, 9, 0, -13, -12, -3, -6, 0, 4, -15, -12], 'class_deg': 25, 'class_size': 3, 'conductor': 550, 'isogeny_matrix': [[1, 25, 5], [25, 1, 5], [5, 5, 1]], 'lmfdb_iso': '550.j', 'trace_hash': 100592759315300363}
• 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': '2.3457840668156523683082783812', 'prec': 100}, 'conductor': 550, 'gens': [], 'heights': [], 'lmfdb_label': '550.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0374564312022390148907210395', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0749128624044780297814420789142585364', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 0], '5': 'a', '7': [0, 0], '11': [1, 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': '550.j2'}
• ec_torsion_growth •

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

  
  
  • id: 24845
    {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '550.j2', 'torsion': [2]}
  • id: 24846
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '550.j2', 'torsion': [5]}
  • id: 24847
    {'degree': 5, 'field': [-176, 0, 0, 0, 0, 1], 'lmfdb_label': '550.j2', 'torsion': [5]}
  • id: 24848
    {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '550.j2', 'torsion': [2, 2]}
  • id: 24849
    {'degree': 8, 'field': [-4, -32, -64, 29, 64, -13, -11, -4, 1], 'lmfdb_label': '550.j2', 'torsion': [3]}
  • id: 24851
    {'degree': 12, 'field': [1, 3, -3, -11, 20, 67, 32, -13, 30, -11, 7, -2, 1], 'lmfdb_label': '550.j2', 'torsion': [10]}
  • id: 24850
    {'degree': 12, 'field': [176, 1232, 1760, 1848, 1448, 492, 320, -30, -33, 4, 14, -6, 1], 'lmfdb_label': '550.j2', 'torsion': [4]}
  • id: 24852
    {'degree': 15, 'field': [176, 704, 176, 2728, -2112, 4940, -4832, 5212, -3184, 2556, -672, 278, -108, 16, -4, 1], 'lmfdb_label': '550.j2', 'torsion': [10]}
  • id: 24855
    {'degree': 20, 'field': [1, -3, 12, -41, 146, 22, 199, 82, 334, -128, 260, -109, 179, -30, 59, -11, 20, -6, 5, -1, 1], 'lmfdb_label': '550.j2', 'torsion': [25]}
  • id: 24854
    {'degree': 20, 'field': [11, 154, 572, -693, -2189, 2062, 2070, -2984, 1242, 442, -454, -2148, 2957, -856, -284, 21, 84, 8, -14, -1, 1], 'lmfdb_label': '550.j2', 'torsion': [25]}
  • id: 24853
    {'degree': 20, 'field': [300125, 42875, -83300, 76020, -23694, -29585, 49400, -73630, 74391, -51510, 32490, -22590, 13086, -5160, 1690, -760, 401, -165, 50, -10, 1], 'lmfdb_label': '550.j2', 'torsion': [5, 5]}
• 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: 6269
    {'conductor': 550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '550.j2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6270
    {'conductor': 550, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '550.j2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6271
    {'conductor': 550, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '550.j2', 'prime': 11, '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: 1668292
    {'adelic_gens': [[1645, 409, 762, 223], [606, 35, 545, 1246], [1, 0, 50, 1], [1, 50, 0, 1], [551, 50, 0, 1], [2151, 50, 2150, 51], [26, 25, 1075, 2176], [38, 41, 1841, 1639]], 'adelic_image': '2200.1200.37.?', 'conductor': 550, 'lmfdb_label': '550.j2', 'prime': 0}
  • id: 2468
    {'conductor': 550, 'elladic_image': '25.120.0.3', 'lmfdb_label': '550.j2', 'modell_image': '5B.1.2', 'prime': 5}
• lmfdb_iso 550.j does not appear in ec_padic