Elliptic curve data - 275.b1

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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': '275b', 'Clabel': '275b3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 171875, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 550, 'ainvs': [0, 1, 1, -195508, -33338481], 'analytic_rank': 0, 'bad_primes': [5, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 275, 'degree': 700, 'elladic_images': ['25.120.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3014280713156973099117450718', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '275.b', 'lmfdb_label': '275.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': 5, 'modell_images': ['5B.1.3'], 'modm_images': ['5.24.0-5.a.2.1', '22.2.0.a.1', '25.120.0-25.a.2.1', '110.48.1.?', '275.600.12.?', '550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[5, 14, 11], [11, 12, 25]], 'sha': 25, 'sha_primes': [5], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540519', 'prec': 103}, 'szpiro_ratio': 8.574976093020473, '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, 2, 1, 2, 0, 2, 2, 0, -2, 0, 1, 2, -4, 4, 0, -4, 2, -4, 0, 0], 'aplist': [2, 1, 0, 2, 1, -4, 2, 0, 1, 0, 7, -3, -8, 6, -8, 6, 5, 12, 7, -3, -4, -10, 6, 15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 275, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '275.b', 'trace_hash': 541839456937515747}
• 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': '0.074061744938238372708320268473', 'prec': 107}, 'conductor': 275, 'gens': [], 'heights': [], 'lmfdb_label': '275.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11352153128177184779858669733', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '25.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8380382820442961949646674333158919314', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  conductor	integer
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'conductor': 275, 'iwdata': {'2': [0, 1, 0], '3': [4, 0], '5': 'a', '7': [0, 0], '11': [1, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0, 0], '23': [2, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '275.b1'}
• ec_torsion_growth •

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

  
  
  • id: 11709
    {'conductor': 275, 'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '275.b1', 'torsion': [2]}
  • id: 11710
    {'conductor': 275, 'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '275.b1', 'torsion': [5]}
  • id: 11711
    {'conductor': 275, 'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '275.b1', 'torsion': [2, 2]}
  • id: 11712
    {'conductor': 275, 'degree': 8, 'field': [11, 44, 77, 63, 3, -6, -2, -2, 1], 'lmfdb_label': '275.b1', 'torsion': [3]}
  • id: 11713
    {'conductor': 275, 'degree': 10, 'field': [-121, 0, 0, 0, 0, -121, 0, 0, 0, 0, 1], 'lmfdb_label': '275.b1', 'torsion': [5]}
  • id: 11714
    {'conductor': 275, 'degree': 12, 'field': [-1034, 264, 660, 396, -788, -196, 276, 172, -102, -14, 6, -2, 1], 'lmfdb_label': '275.b1', 'torsion': [4]}
  • id: 11715
    {'conductor': 275, 'degree': 12, 'field': [1, 1, 2, 4, 7, -8, 3, 2, -3, 2, 0, -1, 1], 'lmfdb_label': '275.b1', 'torsion': [10]}
  • id: 11716
    {'conductor': 275, 'degree': 20, 'field': [20736, -8640, -13680, -4380, 11785, -30338, 12890, 13055, 4555, -11860, 9489, -4380, 815, -35, 20, -77, 70, -35, 15, -5, 1], 'lmfdb_label': '275.b1', 'torsion': [5, 5]}
  • id: 11718
    {'conductor': 275, 'degree': 20, 'field': [1771561, 0, 0, 0, 0, -54571, 0, 0, 0, 0, 1881, 0, 0, 0, 0, -41, 0, 0, 0, 0, 1], 'lmfdb_label': '275.b1', 'torsion': [25]}
  • id: 11717
    {'conductor': 275, 'degree': 20, 'field': [25937424601, 0, 0, 0, 0, -72634001, 0, 0, 0, 0, 227601, 0, 0, 0, 0, -451, 0, 0, 0, 0, 1], 'lmfdb_label': '275.b1', 'torsion': [25]}
• 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: 2524
    {'conductor': 275, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '275.b1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2525
    {'conductor': 275, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '275.b1', '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: 1666920
    {'adelic_gens': [[38, 41, 191, 539], [1, 0, 50, 1], [110, 541, 423, 337], [1, 50, 0, 1], [501, 50, 500, 51], [11, 20, 265, 291]], 'adelic_image': '550.1200.37.?', 'conductor': 275, 'lmfdb_label': '275.b1', 'prime': 0}
  • id: 1143
    {'conductor': 275, 'elladic_image': '25.120.0.4', 'lmfdb_label': '275.b1', 'modell_image': '5B.1.3', 'prime': 5}
• lmfdb_iso 275.b does not appear in ec_padic