Elliptic curve data - 85176.l2

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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': '85176bh', 'Clabel': '85176bh2', 'Cnumber': 2, 'abc_quality': 0.8374478418484275, 'absD': 1191756286925568, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, 13689, -1542294], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 85176, 'degree': 368640, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5754329449315418594888698794', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2], 'jinv': [11664, 49], 'lmfdb_iso': '85176.l', 'lmfdb_label': '85176.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 9, 26], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '28.6.0.d.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 21, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '2.2565964382040631295444243413', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 507], [3, 2, 9464], [7, 8, 12168], [13, 86, 504]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.99309907067360565002912918338', 'prec': 107}, 'szpiro_ratio': 3.701457924670551, '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, -1, 0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, -2, -1, -6, 0, -2, -4, 2, 8, -4, 6, -10, -4, 4, -4, 12, -2, -12, -6, 2, -8, 0, 14, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 85176, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '85176.l', 'trace_hash': 94530561868720191}
• 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': '0.042815037704656648498697931224', 'prec': 107}, 'conductor': 85176, 'gens': [[429, 9126, 1], [91, 676, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1510033699329495496659500860', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.9865797511014959296553800846', 'prec': 100}], 'lmfdb_label': '85176.l2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.24626330314192750139677537342', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.8914702836870570949966772155138278307', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[78, 0, 1]], 'xcoord_integral_points': [78, 91, 103, 105, 169, 321, 429, 1261, 2535, 18850, 1005801]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [4, 0], '7': [2, 0], '11': [2, 0], '13': 'a', '17': [2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '85176.l2'}
• ec_torsion_growth •

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

  
  
  • id: 3993656
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '85176.l2', 'torsion': [2, 2]}
  • id: 3993657
    {'degree': 4, 'field': [-507, 0, 39, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [4]}
  • id: 3993660
    {'degree': 8, 'field': [-1041, -504, -1438, -474, -66, -50, -6, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [6]}
  • id: 3993658
    {'degree': 8, 'field': [1369, 0, 547, 0, 135, 0, 19, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [2, 4]}
  • id: 3993659
    {'degree': 8, 'field': [257049, 0, 19773, 0, 2028, 0, -39, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [2, 4]}
  • id: 3993662
    {'degree': 16, 'field': [1083681, -524664, -1242942, 262116, 1760242, -667134, 117060, 109492, -26931, 2892, -772, 174, 102, -100, 6, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [2, 6]}
  • id: 3993661
    {'degree': 16, 'field': [46027411600, 0, -22146655264, 0, 2443848752, 0, -9724912, 0, -6845864, 0, -29768, 0, 6332, 0, 148, 0, 1], 'lmfdb_label': '85176.l2', 'torsion': [8]}
• 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: 2077227
    {'conductor': 85176, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '85176.l2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2077228
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '85176.l2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2077229
    {'conductor': 85176, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '85176.l2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2077230
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85176.l2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2225144
    {'adelic_gens': [[1, 2, 2, 5], [3, 4, 8, 11], [81, 4, 80, 5], [32, 1, 55, 0], [1, 4, 0, 1], [65, 22, 20, 63], [73, 4, 62, 9], [1, 0, 4, 1]], 'adelic_image': '84.12.0.?', 'conductor': 85176, 'lmfdb_label': '85176.l2', 'prime': 0}
  • id: 347688
    {'conductor': 85176, 'elladic_image': '2.3.0.1', 'lmfdb_label': '85176.l2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4397558
    {'lmfdb_iso': '85176.l', 'p': 5, 'prec': 20, 'unit': 654364466739, 'val': 3}
  • id: 4397565
    {'lmfdb_iso': '85176.l', 'p': 11, 'prec': 20, 'unit': 30768978198791716611, 'val': 2}
  • id: 4397566
    {'lmfdb_iso': '85176.l', 'p': 17, 'prec': 20, 'unit': 122141475069260835461023, 'val': 2}
  • id: 4397567
    {'lmfdb_iso': '85176.l', 'p': 19, 'prec': 20, 'unit': 598297203655069222707593, 'val': 2}
  • id: 4397571
    {'lmfdb_iso': '85176.l', 'p': 23, 'prec': 20, 'unit': 66509483872944968530057311, 'val': 2}
  • id: 4397563
    {'lmfdb_iso': '85176.l', 'p': 29, 'prec': 20, 'unit': 4324891397300436034742650681, 'val': 2}
  • id: 4397560
    {'lmfdb_iso': '85176.l', 'p': 31, 'prec': 20, 'unit': 11437698358331454825013523386, 'val': 2}
  • id: 4397575
    {'lmfdb_iso': '85176.l', 'p': 37, 'prec': 20, 'unit': 191549533555055773103242298635, 'val': 2}
  • id: 4397561
    {'lmfdb_iso': '85176.l', 'p': 41, 'prec': 20, 'unit': 3721163245414770845807737208860, 'val': 2}
  • id: 4397562
    {'lmfdb_iso': '85176.l', 'p': 43, 'prec': 20, 'unit': 10362478385966395999833050009243, 'val': 2}
  • id: 4397573
    {'lmfdb_iso': '85176.l', 'p': 47, 'prec': 20, 'unit': 48498784818640710156420079326771, 'val': 2}
  • id: 4397568
    {'lmfdb_iso': '85176.l', 'p': 53, 'prec': 20, 'unit': 297931822518941811539666606115415, 'val': 2}
  • id: 4397569
    {'lmfdb_iso': '85176.l', 'p': 59, 'prec': 20, 'unit': 3118487009497185892049447462824603, 'val': 2}
  • id: 4397574
    {'lmfdb_iso': '85176.l', 'p': 61, 'prec': 20, 'unit': 2610911216023021082398251588867154, 'val': 2}
  • id: 4397557
    {'lmfdb_iso': '85176.l', 'p': 67, 'prec': 20, 'unit': 21097113751659212484858094449418186, 'val': 2}
  • id: 4397559
    {'lmfdb_iso': '85176.l', 'p': 71, 'prec': 20, 'unit': 9517085491406259083723757124832499, 'val': 2}
  • id: 4397570
    {'lmfdb_iso': '85176.l', 'p': 73, 'prec': 20, 'unit': 75509827924156397283766767250727216, 'val': 2}
  • id: 4397564
    {'lmfdb_iso': '85176.l', 'p': 79, 'prec': 20, 'unit': 315623424317227047457754667809729911, 'val': 2}
  • id: 4397572
    {'lmfdb_iso': '85176.l', 'p': 89, 'prec': 20, 'unit': 3184962501327783813815713316119383826, 'val': 2}
  • id: 4397556
    {'lmfdb_iso': '85176.l', 'p': 97, 'prec': 20, 'unit': 53657809436443592881732477814205563020, 'val': 2}