Elliptic curve data - 2275.e1

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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': '2275c', 'Clabel': '2275c3', 'Cnumber': 3, 'abc_quality': 1.0588031094756087, 'absD': 5854876015625, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 7280, 'ainvs': [1, -1, 0, -9917, -359384], 'analytic_rank': 0, 'bad_primes': [5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2275, 'degree': 3072, 'elladic_images': ['8.12.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2058476381255177545890403219', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [6903498885921, 374712065], 'lmfdb_iso': '2275.e', 'lmfdb_label': '2275.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -397, -2796], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '20.12.0-4.c.1.1', '40.24.0-8.o.1.3', '52.12.0-4.c.1.1', '104.24.0.?', '112.24.0.?', '130.6.0.?', '260.24.0.?', '520.96.0.?', '560.48.0.?', '1456.48.0.?', '7280.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 325], [5, 18, 91], [7, 8, 325], [13, 14, 175]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.40112868190846756728866065529', 'prec': 103}, 'szpiro_ratio': 5.073870614855939, '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, 1, 0, -1, 0, 0, 1, -3, -3, 0, 0, 0, -1, 1, 0, -1, 6, -3, 0, 0], 'aplist': [1, 0, 0, 1, 0, -1, 6, 0, 4, -2, -4, 10, 2, 8, 0, 2, 0, -2, 4, 12, 6, 8, -4, 2, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 2275, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '2275.e', 'trace_hash': 1137927232190697775}
• 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': '0.089663161826330435019240056534', 'prec': 107}, 'conductor': 2275, 'gens': [], 'heights': [], 'lmfdb_label': '2275.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.48002965406120816920336694671', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9201186162448326768134677868416193472', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-269, 269, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 2], '5': 'a', '7': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '2275.e1'}
• ec_torsion_growth •

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

  
  
  • id: 115059
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 2]}
  • id: 115060
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [4]}
  • id: 115061
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [4]}
  • id: 115062
    {'degree': 4, 'field': [4, 0, 9, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 4]}
  • id: 115066
    {'degree': 8, 'field': [-651, -1491, -1155, -543, -225, -48, -3, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [6]}
  • id: 115064
    {'degree': 8, 'field': [169, 0, 52, 0, 23, 0, -4, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [8]}
  • id: 115063
    {'degree': 8, 'field': [3771, 1044, -1168, 252, -135, 8, 2, -4, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 4]}
  • id: 115065
    {'degree': 8, 'field': [828100, 0, 50700, 0, 1365, 0, 0, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 8]}
  • id: 115067
    {'degree': 16, 'field': [1, 0, 0, 0, -126, 0, 0, 0, 5011, 0, 0, 0, -126, 0, 0, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [4, 4]}
  • id: 115068
    {'degree': 16, 'field': [1, 0, 0, 0, 33, 0, 0, 0, 128, 0, 0, 0, 33, 0, 0, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 8]}
  • id: 115069
    {'degree': 16, 'field': [2304, 0, 5255424, 0, -1605600, 0, 137952, 0, -15315, 0, 4587, 0, -438, 0, 0, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [2, 6]}
  • id: 115070
    {'degree': 16, 'field': [34969, 0, 1713418, 0, 759265, 0, 177976, 0, 41470, 0, 7234, 0, 688, 0, 40, 0, 1], 'lmfdb_label': '2275.e1', 'torsion': [12]}
  • id: 115071
    {'degree': 16, 'field': [216178249, 262938564, 557868752, 368003958, 386839801, 128849628, 64605455, 11005404, 3950206, 220542, 127652, -3294, 3901, -96, 98, 0, 1], 'lmfdb_label': '2275.e1', '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: 38066
    {'conductor': 2275, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2275.e1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 38067
    {'conductor': 2275, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '2275.e1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 38068
    {'conductor': 2275, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2275.e1', '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: 1678690
    {'adelic_gens': [[4161, 16, 4168, 129], [1, 16, 0, 1], [1, 8, 8, 65], [3647, 3650, 1794, 1783], [7265, 16, 7264, 17], [574, 3, 1213, 20], [7, 3656, 2978, 6937], [1, 0, 16, 1], [1442, 7277, 2819, 7260], [15, 166, 6994, 4115]], 'adelic_image': '7280.192.3.?', 'conductor': 2275, 'lmfdb_label': '2275.e1', 'prime': 0}
  • id: 11133
    {'conductor': 2275, 'elladic_image': '8.12.0.10', 'lmfdb_label': '2275.e1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 2275.e does not appear in ec_padic