Elliptic curve data - 248768.t1

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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': '248768t', 'Clabel': '248768t2', 'Cnumber': 2, 'abc_quality': 0.87184842279915, 'absD': 60137251945472, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 7176, 'ainvs': [0, -1, 0, -12393, -644879], 'analytic_rank': 1, 'bad_primes': [2, 13, 23], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 248768, 'degree': 449280, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3590850926291641618974389653', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 19, 'isogeny_degrees': [1, 3], 'jinv': [-42592000, 12167], 'lmfdb_iso': '248768.t', 'lmfdb_label': '248768.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -18, -43], 'min_quad_twist_disc': 104, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '46.2.0.a.1', '138.8.0.?', '312.8.0.?', '7176.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '14.039598161744247010689771166', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3887], [3, 2, 10816], [13, 86, 1472], [23, 24, 10816]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50101223656822529731033152337', 'prec': 107}, 'szpiro_ratio': 3.242808878969331, '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, 0, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0], 'aplist': [0, -1, 0, -2, 0, 0, -6, 2, -1, 3, -5, 8, -3, -8, -9, -6, -12, -14, 8, 15, 7, -10, 6, 0, 10], 'class_deg': 3, 'class_size': 2, 'conductor': 248768, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '248768.t', 'trace_hash': 835651608197389980}
• 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': '0.065995403372102813646638169085', 'prec': 107}, 'conductor': 248768, 'gens': [[833128, 122573645, 79]], 'heights': [{'__RealLiteral__': 0, 'data': '14.039598161744247010689771166', 'prec': 100}], 'lmfdb_label': '248768.t1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22294432784250105642703886713', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1300487753488845790006338408726207240', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 248768.t1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10712611
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '248768.t1', 'torsion': [3]}
  • id: 10712612
    {'degree': 3, 'field': [1, 0, -1, 1], 'lmfdb_label': '248768.t1', 'torsion': [2]}
  • id: 10712614
    {'degree': 6, 'field': [-4394, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '248768.t1', 'torsion': [3]}
  • id: 10712613
    {'degree': 6, 'field': [1, -3, 5, -5, 5, -3, 1], 'lmfdb_label': '248768.t1', 'torsion': [2, 2]}
  • id: 10712615
    {'degree': 6, 'field': [480793, -12636, 18406, -310, 235, -2, 1], 'lmfdb_label': '248768.t1', 'torsion': [6]}
  • id: 10712616
    {'degree': 12, 'field': [-111016607, 0, -5940688, 0, 171366, 0, -21970, 0, -1859, 0, 0, 0, 1], 'lmfdb_label': '248768.t1', 'torsion': [4]}
  • id: 10712617
    {'degree': 12, 'field': [19298449, 26358, 65931, -175810, 66000, 26238, -8647, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '248768.t1', 'torsion': [3, 3]}
  • id: 10712618
    {'degree': 12, 'field': [222493260991, -17318239854, 17878058347, -1129249720, 588749135, -29208434, 10169735, -374486, 97175, -2380, 487, -6, 1], 'lmfdb_label': '248768.t1', 'torsion': [2, 6]}
  • id: 10712620
    {'degree': 18, 'field': [-84874631425, 463558212, -869616546, 774003106, 286510785, -111308838, 53971497, 2821008, -2109165, 834820, -131736, 52698, -13226, 54, -15, -14, 15, -6, 1], 'lmfdb_label': '248768.t1', 'torsion': [6]}
  • id: 10712619
    {'degree': 18, 'field': [205882411091556447, 3897039114028674, 19192459279073139, 225937706734134, 821683941140169, 5612563580454, 21239336172748, 74533079502, 365379727122, 512739920, 4339470051, 996084, 35609169, -8694, 194967, -46, 648, 0, 1], 'lmfdb_label': '248768.t1', 'torsion': [9]}
• 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: 6168176
    {'conductor': 248768, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '248768.t1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6168177
    {'conductor': 248768, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '248768.t1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6168178
    {'conductor': 248768, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '248768.t1', 'prime': 23, '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: 3243530
    {'adelic_gens': [[7171, 6, 7170, 7], [4, 3, 9, 7], [4835, 546, 4836, 545], [5381, 0, 0, 7175], [5617, 6630, 2223, 5539], [1103, 0, 0, 7175], [3587, 0, 0, 7175], [1078, 7059, 5993, 545], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '7176.16.0.?', 'conductor': 248768, 'lmfdb_label': '248768.t1', 'prime': 0}
  • id: 898401
    {'conductor': 248768, 'elladic_image': '3.4.0.1', 'lmfdb_label': '248768.t1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 248768.t does not appear in ec_padic