Elliptic curve data - 312.d2

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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': '312f', 'Clabel': '312f1', 'Cnumber': 1, 'abc_quality': 0.9673858851013342, 'absD': 73008, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 1, 0, 5, 14], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 312, 'degree': 48, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.38504079149495045748205545934', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [702464, 4563], 'lmfdb_iso': '312.d', 'lmfdb_label': '312.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 5, 14], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '52.6.0.c.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.20762904080581622019503964056', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 104], [13, 14, 24]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61608985168159889395446616649', 'prec': 107}, 'szpiro_ratio': 3.231712095971987, '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, 0, 1, 0, -4, 0, -4, 0, 1, 0, -2, 0, -1, 0, -4, 0, -6, 0, 4, 0], 'aplist': [0, 1, -4, -4, -2, -1, -6, 4, 4, -6, 8, -10, -4, -4, -6, 6, -6, -6, 0, 10, -2, 0, -10, 8, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 312, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '312.d', 'trace_hash': 1530564864511384045}
• 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': '2.1599424611610504407261538091', 'prec': 100}, 'conductor': 312, 'gens': [[-1, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.20762904080581622019503964056', 'prec': 103}], 'lmfdb_label': '312.d2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5056872215369941418147206789', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5607603031013504720016975709553043934', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-2, 0, 1]], 'xcoord_integral_points': [-2, -1, 2, 7, 11, 206]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [3, 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': '312.d2'}
• ec_torsion_growth •

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

  
  
  • id: 13148
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '312.d2', 'torsion': [2, 2]}
  • id: 13149
    {'degree': 4, 'field': [1, -1, -1, -1, 1], 'lmfdb_label': '312.d2', 'torsion': [4]}
  • id: 13152
    {'degree': 8, 'field': [-27, 0, -40, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '312.d2', 'torsion': [6]}
  • id: 13150
    {'degree': 8, 'field': [1, -1, 2, 3, -1, 3, 2, -1, 1], 'lmfdb_label': '312.d2', 'torsion': [2, 4]}
  • id: 13151
    {'degree': 8, 'field': [57, -144, 132, -42, -17, 22, -6, -2, 1], 'lmfdb_label': '312.d2', 'torsion': [2, 4]}
  • id: 13153
    {'degree': 16, 'field': [81, 0, 306, 0, -591, 0, 154, 0, 156, 0, -34, 0, -31, 0, 6, 0, 1], 'lmfdb_label': '312.d2', 'torsion': [8]}
  • id: 13154
    {'degree': 16, 'field': [81, 162, 432, 486, 594, 396, 360, 162, 255, -12, 168, -78, 78, -30, 16, -4, 1], 'lmfdb_label': '312.d2', 'torsion': [2, 6]}
• 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: 2912
    {'conductor': 312, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '312.d2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2913
    {'conductor': 312, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '312.d2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2914
    {'conductor': 312, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '312.d2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1667063
    {'adelic_gens': [[1, 2, 2, 5], [145, 4, 134, 9], [106, 1, 103, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 312, 'lmfdb_label': '312.d2', 'prime': 0}
  • id: 1268
    {'conductor': 312, 'elladic_image': '2.3.0.1', 'lmfdb_label': '312.d2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3427
    {'lmfdb_iso': '312.d', 'p': 5, 'prec': 20, 'unit': 18021149105687, 'val': -1}
  • id: 3428
    {'lmfdb_iso': '312.d', 'p': 7, 'prec': 20, 'unit': 6469190464811330, 'val': 1}
  • id: 3426
    {'lmfdb_iso': '312.d', 'p': 11, 'prec': 20, 'unit': 2885201213660238354, 'val': 2}
  • id: 3434
    {'lmfdb_iso': '312.d', 'p': 17, 'prec': 20, 'unit': 196340172287566511155359, 'val': 1}
  • id: 3424
    {'lmfdb_iso': '312.d', 'p': 19, 'prec': 20, 'unit': 1004872569921456617964127, 'val': 1}
  • id: 3438
    {'lmfdb_iso': '312.d', 'p': 23, 'prec': 20, 'unit': 31770664299240452821246675, 'val': 1}
  • id: 3432
    {'lmfdb_iso': '312.d', 'p': 29, 'prec': 20, 'unit': 1917082934008994752811347441, 'val': 1}
  • id: 3429
    {'lmfdb_iso': '312.d', 'p': 31, 'prec': 20, 'unit': 7157123376936915747775390501, 'val': 1}
  • id: 3443
    {'lmfdb_iso': '312.d', 'p': 37, 'prec': 20, 'unit': 284292406000466599814829149872, 'val': 1}
  • id: 3430
    {'lmfdb_iso': '312.d', 'p': 41, 'prec': 20, 'unit': 2048047203559616663111091839846, 'val': 1}
  • id: 3431
    {'lmfdb_iso': '312.d', 'p': 43, 'prec': 20, 'unit': 2202914062233220842223353304145, 'val': 1}
  • id: 3433
    {'lmfdb_iso': '312.d', 'p': 47, 'prec': 20, 'unit': 38274064848476334808710336287096, 'val': 1}
  • id: 3436
    {'lmfdb_iso': '312.d', 'p': 53, 'prec': 20, 'unit': 9600444273673449185270066309947, 'val': 2}
  • id: 3441
    {'lmfdb_iso': '312.d', 'p': 59, 'prec': 20, 'unit': 593004088852083863237499889735450, 'val': 1}
  • id: 3442
    {'lmfdb_iso': '312.d', 'p': 61, 'prec': 20, 'unit': 5894429253277080140571196376329911, 'val': 1}
  • id: 3440
    {'lmfdb_iso': '312.d', 'p': 71, 'prec': 20, 'unit': 91358900403527379929901444834857658, 'val': 1}
  • id: 3437
    {'lmfdb_iso': '312.d', 'p': 73, 'prec': 20, 'unit': 202959259429033351718805677049041543, 'val': 1}
  • id: 3435
    {'lmfdb_iso': '312.d', 'p': 83, 'prec': 20, 'unit': 2756665949202667867836604599559502097, 'val': 1}
  • id: 3439
    {'lmfdb_iso': '312.d', 'p': 89, 'prec': 20, 'unit': 8083300679383828972635141397016577490, 'val': 1}
  • id: 3425
    {'lmfdb_iso': '312.d', 'p': 97, 'prec': 20, 'unit': 13184326673666078417176514744042462571, 'val': 1}