Elliptic curve data - 275.a4

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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': '275a', 'Clabel': '275a1', 'Cnumber': 1, 'abc_quality': 0.7920712085843463, 'absD': 859375, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [1, -1, 1, 20, 22], 'analytic_rank': 1, 'bad_primes': [5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 275, 'degree': 24, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.17409370431765402277983986448', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [59319, 55], 'lmfdb_iso': '275.a', 'lmfdb_label': '275.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 1, 0], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '40.24.0-40.z.1.4', '88.24.0.?', '110.6.0.?', '220.24.0.?', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3844904924265576284815496429', 'prec': 100}, 'semistable': False, 'serre_invariants': [[5, 18, 11], [11, 12, 25]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.97881266053470421008021953109', 'prec': 107}, 'szpiro_ratio': 3.676011013083879, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, -1, 0, 0, 0, 3, -3, 0, -1, 0, -2, 0, 0, -1, -6, 3, -4, 0], 'aplist': [-1, 0, 0, 0, -1, -2, -6, -4, -4, 6, -8, 2, 2, -4, 12, 2, 4, -10, 16, 8, -14, 8, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 275, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '275.a', 'trace_hash': 161217989908240353}
• 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': '1.4164976887652323834412748915', 'prec': 100}, 'conductor': 275, 'gens': [[8, 21, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3844904924265576284815496429', 'prec': 100}], 'lmfdb_label': '275.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8401405798554902509168216721', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0969494293484273097814192758128800949', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[4, 10, 1]], 'xcoord_integral_points': [-1, 4, 8, 79]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 1, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '275.a4'}
• ec_torsion_growth •

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

  
  
  • id: 11641
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '275.a4', 'torsion': [2, 4]}
  • id: 11642
    {'degree': 4, 'field': [-4, 4, 1, -1, 1], 'lmfdb_label': '275.a4', 'torsion': [8]}
  • id: 11646
    {'degree': 8, 'field': [1, -4, 4, -1, -5, -1, 4, -4, 1], 'lmfdb_label': '275.a4', 'torsion': [12]}
  • id: 11645
    {'degree': 8, 'field': [1, 0, -7, 0, 28, 0, -7, 0, 1], 'lmfdb_label': '275.a4', 'torsion': [2, 8]}
  • id: 11644
    {'degree': 8, 'field': [1, 0, -1, 0, 16, 0, -1, 0, 1], 'lmfdb_label': '275.a4', 'torsion': [2, 8]}
  • id: 11643
    {'degree': 8, 'field': [676, 0, -131, 0, 431, 0, -41, 0, 1], 'lmfdb_label': '275.a4', 'torsion': [4, 4]}
  • id: 11648
    {'degree': 16, 'field': [9, 0, -117, 0, 540, 0, -234, 0, 30, 0, 39, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '275.a4', 'torsion': [2, 12]}
  • id: 11647
    {'degree': 16, 'field': [25, 200, 600, 900, 875, 900, 900, 500, 165, 160, 80, -80, -95, -40, -10, 0, 1], 'lmfdb_label': '275.a4', 'torsion': [16]}
• 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: 2512
    {'conductor': 275, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '275.a4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2513
    {'conductor': 275, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '275.a4', '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: 1666919
    {'adelic_gens': [[169, 168, 398, 175], [1, 0, 8, 1], [368, 3, 285, 2], [433, 8, 432, 9], [1, 8, 0, 1], [1, 4, 4, 17], [172, 439, 329, 434], [7, 6, 434, 435], [59, 58, 178, 395]], 'adelic_image': '440.48.0.?', 'conductor': 275, 'lmfdb_label': '275.a4', 'prime': 0}
  • id: 1142
    {'conductor': 275, 'elladic_image': '4.12.0.7', 'lmfdb_label': '275.a4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2723
    {'lmfdb_iso': '275.a', 'p': 13, 'prec': 20, 'unit': 1126291728239330729250, 'val': 1}
  • id: 2725
    {'lmfdb_iso': '275.a', 'p': 17, 'prec': 20, 'unit': 211215701859629545401121, 'val': 1}
  • id: 2726
    {'lmfdb_iso': '275.a', 'p': 19, 'prec': 20, 'unit': 396423802552825977087858, 'val': 1}
  • id: 2730
    {'lmfdb_iso': '275.a', 'p': 23, 'prec': 20, 'unit': 51167599521647343510161310, 'val': 1}
  • id: 2722
    {'lmfdb_iso': '275.a', 'p': 29, 'prec': 20, 'unit': 1831597592460100793950312897, 'val': 1}
  • id: 2734
    {'lmfdb_iso': '275.a', 'p': 31, 'prec': 20, 'unit': 21141168928157756153981608387, 'val': 1}
  • id: 2718
    {'lmfdb_iso': '275.a', 'p': 37, 'prec': 20, 'unit': 310855361780438099994513197438, 'val': 1}
  • id: 2720
    {'lmfdb_iso': '275.a', 'p': 41, 'prec': 20, 'unit': 3120371680091086457562410295022, 'val': 1}
  • id: 2721
    {'lmfdb_iso': '275.a', 'p': 43, 'prec': 20, 'unit': 8948960138731778663899303612330, 'val': 1}
  • id: 2732
    {'lmfdb_iso': '275.a', 'p': 47, 'prec': 20, 'unit': 15210386388318564994746553103915, 'val': 1}
  • id: 2727
    {'lmfdb_iso': '275.a', 'p': 53, 'prec': 20, 'unit': 121917195610826292075103805133356, 'val': 1}
  • id: 2728
    {'lmfdb_iso': '275.a', 'p': 59, 'prec': 20, 'unit': 3821734023305687113338625239234238, 'val': 1}
  • id: 2733
    {'lmfdb_iso': '275.a', 'p': 61, 'prec': 20, 'unit': 1623688254472073051805656241404443, 'val': 1}
  • id: 2717
    {'lmfdb_iso': '275.a', 'p': 67, 'prec': 20, 'unit': 17435329800343115624852340241709739, 'val': 1}
  • id: 2719
    {'lmfdb_iso': '275.a', 'p': 71, 'prec': 20, 'unit': 81216796435215868508357896539721290, 'val': 1}
  • id: 2729
    {'lmfdb_iso': '275.a', 'p': 73, 'prec': 20, 'unit': 218199332991026766842577208646348497, 'val': 1}
  • id: 2724
    {'lmfdb_iso': '275.a', 'p': 79, 'prec': 20, 'unit': 598143295772279058995444295432495633, 'val': 1}
  • id: 2716
    {'lmfdb_iso': '275.a', 'p': 83, 'prec': 20, 'unit': 2034744318818201055151375512889821901, 'val': 1}
  • id: 2731
    {'lmfdb_iso': '275.a', 'p': 89, 'prec': 20, 'unit': 644756966347566851542669527308515713, 'val': 1}
  • id: 2715
    {'lmfdb_iso': '275.a', 'p': 97, 'prec': 20, 'unit': 45481114684074856781871975812875511091, 'val': 1}