Elliptic curve data - 77616.ff1

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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': '77616bp', 'Clabel': '77616bp2', 'Cnumber': 2, 'abc_quality': 1.043588000933414, 'absD': 33019780401923359435776, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 308, 'ainvs': [0, 0, 0, -10051419, -8602937350], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 77616, 'degree': 4423680, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0267873641513913699050232615', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 135, 'isogeny_degrees': [1, 2], 'jinv': [1278763167594532, 375974556419], 'lmfdb_iso': '77616.ff', 'lmfdb_label': '77616.ff1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -22792, 936540], 'min_quad_twist_disc': -84, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '44.6.0.a.1', '308.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '22.758603502996517591995901845', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 4851], [3, 6, 784], [7, 32, 1584], [11, 12, 7056]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.92690349482305878047369750343', 'prec': 103}, 'szpiro_ratio': 5.327334460641313, '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, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 4, 0], 'aplist': [0, 0, 2, 0, -1, 0, 4, 4, -4, -2, -2, -6, 4, 4, -2, -2, 6, -4, 0, -12, -16, 8, 12, 10, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 77616, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '77616.ff', 'trace_hash': 2099720857233699391}
• 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': '0.0023494483376912002084164469620', 'prec': 110}, 'conductor': 77616, 'gens': [[-115598746550, 19831349452702410, 7219]], 'heights': [{'__RealLiteral__': 0, 'data': '22.758603502996517591995901845', 'prec': 100}], 'lmfdb_label': '77616.ff1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.086704424646178522099778941053', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.8930864899112644337640533837179061930', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-938, 0, 1]], 'xcoord_integral_points': [-938]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 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': '77616.ff1'}
• ec_torsion_growth •

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

  
  
  • id: 3665209
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '77616.ff1', 'torsion': [2, 2]}
  • id: 3665210
    {'degree': 4, 'field': [22, -8, 11, -1, 1], 'lmfdb_label': '77616.ff1', 'torsion': [4]}
  • id: 3665213
    {'degree': 8, 'field': [-132, -336, 120, 12, 60, -36, 2, -2, 1], 'lmfdb_label': '77616.ff1', 'torsion': [6]}
  • id: 3665211
    {'degree': 8, 'field': [784, 1008, -2784, -952, -314, 216, -20, -2, 1], 'lmfdb_label': '77616.ff1', 'torsion': [2, 4]}
  • id: 3665212
    {'degree': 8, 'field': [4041, -1026, 726, -396, 67, -28, 14, -2, 1], 'lmfdb_label': '77616.ff1', 'torsion': [2, 4]}
  • id: 3665214
    {'degree': 16, 'field': [1269997, 2296766, 2278387, 2773370, 1420760, 1069786, 929591, -120454, 253738, -45374, 28377, -3890, 1744, -154, 61, -2, 1], 'lmfdb_label': '77616.ff1', 'torsion': [8]}
  • id: 3665215
    {'degree': 16, 'field': [1960452729, 0, -456087996, 0, 57329532, 0, -5845776, 0, 453594, 0, -26424, 0, 1324, 0, -52, 0, 1], 'lmfdb_label': '77616.ff1', '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: 1888206
    {'conductor': 77616, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '77616.ff1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1888207
    {'conductor': 77616, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '77616.ff1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1888208
    {'conductor': 77616, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '77616.ff1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1888209
    {'conductor': 77616, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '77616.ff1', '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: 2176652
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [45, 4, 90, 9], [114, 1, 251, 0], [232, 81, 77, 232], [305, 4, 304, 5]], 'adelic_image': '308.12.0.?', 'conductor': 77616, 'lmfdb_label': '77616.ff1', 'prime': 0}
  • id: 320198
    {'conductor': 77616, 'elladic_image': '2.3.0.1', 'lmfdb_label': '77616.ff1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3995769
    {'lmfdb_iso': '77616.ff', 'p': 5, 'prec': 20, 'unit': 6898224380653, 'val': 1}
  • id: 3995776
    {'lmfdb_iso': '77616.ff', 'p': 17, 'prec': 20, 'unit': 177679732486327922388855, 'val': 1}
  • id: 3995766
    {'lmfdb_iso': '77616.ff', 'p': 19, 'prec': 20, 'unit': 1089719293210939472078157, 'val': 1}
  • id: 3995780
    {'lmfdb_iso': '77616.ff', 'p': 23, 'prec': 20, 'unit': 26136989574989359817913765, 'val': 1}
  • id: 3995774
    {'lmfdb_iso': '77616.ff', 'p': 29, 'prec': 20, 'unit': 6023035678327739593330782830, 'val': 1}
  • id: 3995771
    {'lmfdb_iso': '77616.ff', 'p': 31, 'prec': 20, 'unit': 19767414363042791497545199103, 'val': 1}
  • id: 3995784
    {'lmfdb_iso': '77616.ff', 'p': 37, 'prec': 20, 'unit': 471319701630384511291053768606, 'val': 1}
  • id: 3995772
    {'lmfdb_iso': '77616.ff', 'p': 41, 'prec': 20, 'unit': 2513589989857787413757515421028, 'val': 1}
  • id: 3995773
    {'lmfdb_iso': '77616.ff', 'p': 43, 'prec': 20, 'unit': 9888644645338153872176373158093, 'val': 1}
  • id: 3995782
    {'lmfdb_iso': '77616.ff', 'p': 47, 'prec': 20, 'unit': 31073319879828364581617980267981, 'val': 1}
  • id: 3995778
    {'lmfdb_iso': '77616.ff', 'p': 53, 'prec': 20, 'unit': 335664434869142085631793912320614, 'val': 1}
  • id: 3995768
    {'lmfdb_iso': '77616.ff', 'p': 59, 'prec': 20, 'unit': 3389144784743211400849180941562133, 'val': 1}
  • id: 3995783
    {'lmfdb_iso': '77616.ff', 'p': 61, 'prec': 20, 'unit': 4529440299347856667694586551358705, 'val': 1}
  • id: 3995770
    {'lmfdb_iso': '77616.ff', 'p': 71, 'prec': 20, 'unit': 1093369500808962510653418636826495, 'val': 2}
  • id: 3995779
    {'lmfdb_iso': '77616.ff', 'p': 73, 'prec': 20, 'unit': 11074572358180715533413574080410524, 'val': 1}
  • id: 3995775
    {'lmfdb_iso': '77616.ff', 'p': 79, 'prec': 20, 'unit': 1127147416635613294469944467652538257, 'val': 1}
  • id: 3995777
    {'lmfdb_iso': '77616.ff', 'p': 83, 'prec': 20, 'unit': 477018750881618100518428633060746289, 'val': 1}
  • id: 3995781
    {'lmfdb_iso': '77616.ff', 'p': 89, 'prec': 20, 'unit': 8248642787971161304583510589832741326, 'val': 1}
  • id: 3995767
    {'lmfdb_iso': '77616.ff', 'p': 97, 'prec': 20, 'unit': 37841356174539576388135480416306256840, 'val': 1}