Elliptic curve data - 49686.h2

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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': '49686i', 'Clabel': '49686i1', 'Cnumber': 1, 'abc_quality': 1.0387829692161805, 'absD': 1701910583588443841069184, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 2184, 'ainvs': [1, 1, 0, 5912462, 62524364596], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 49686, 'degree': 9483264, 'elladic_images': ['7.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3290223527574847931517375845', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 7, 'isogeny_degrees': [1, 7], 'jinv': [40251338884511, 2997011332224], 'lmfdb_iso': '49686.h', 'lmfdb_label': '49686.h2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 714, -82908], 'min_quad_twist_disc': -91, 'modell_images': ['7B.6.1'], 'modm_images': ['7.24.0.a.1', '91.48.0.?', '168.48.0.?', '2184.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 24843], [3, 4, 16562], [7, 26, 169], [13, 98, 294]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0735925994990597725723174920', 'prec': 100}, 'szpiro_ratio': 5.848322641064215, '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, -1, -1, 1, -1, 1, 0, -1, 1, 1, -5, -1, 0, 0, 1, 1, 3, -1, -1, -1], 'aplist': [-1, -1, -1, 0, -5, 0, 3, -1, 3, 9, 4, 11, 0, -5, -8, -2, 4, 15, 2, 12, 11, 10, -14, 6, -14], 'class_deg': 7, 'class_size': 2, 'conductor': 49686, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '49686.h', 'trace_hash': 2037581289998857060}
• 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': '0.0012836538394380720748074858771', 'prec': 110}, 'conductor': 49686, 'gens': [], 'heights': [], 'lmfdb_label': '49686.h2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.064169766985974595578462070697', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0267162717755935292553931311556271459', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '11': [0, 0], '13': 'a', '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '49686.h2'}
• ec_torsion_growth •

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

  
  
  • id: 2415567
    {'degree': 2, 'field': [23, -1, 1], 'lmfdb_label': '49686.h2', 'torsion': [7]}
  • id: 2415568
    {'degree': 3, 'field': [-9, 13, -1, 1], 'lmfdb_label': '49686.h2', 'torsion': [2]}
  • id: 2415570
    {'degree': 6, 'field': [9, -27, 40, -35, 14, -1, 1], 'lmfdb_label': '49686.h2', 'torsion': [14]}
  • id: 2415569
    {'degree': 6, 'field': [2328, -2136, 574, -20, -3, -2, 1], 'lmfdb_label': '49686.h2', 'torsion': [2, 2]}
  • id: 2415571
    {'degree': 8, 'field': [-1862, -175, -2120, -2067, 81, -267, -5, -4, 1], 'lmfdb_label': '49686.h2', 'torsion': [3]}
  • id: 2415572
    {'degree': 12, 'field': [-607698, -304138, -41013, -34980, -5347, 29116, -7090, -1320, 1064, -170, 11, -4, 1], 'lmfdb_label': '49686.h2', 'torsion': [4]}
  • id: 2415573
    {'degree': 12, 'field': [9216, 0, 1920, 0, 26128, 0, 6000, 0, 668, 0, 36, 0, 1], 'lmfdb_label': '49686.h2', 'torsion': [2, 14]}
  • id: 2415574
    {'degree': 16, 'field': [71631044, -59699800, -13776929, 4433694, 4275073, 2011870, 1100842, -411868, 352224, -101890, 18914, -5498, 1226, -168, 53, -4, 1], 'lmfdb_label': '49686.h2', 'torsion': [21]}
• 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: 1188348
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '49686.h2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1188349
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '49686.h2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1188350
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '49686.h2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1188351
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '49686.h2', '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: 1994792
    {'adelic_gens': [[1093, 14, 1099, 99], [8, 5, 91, 57], [1, 14, 0, 1], [2171, 14, 2170, 15], [1639, 14, 553, 99], [1, 0, 14, 1], [167, 2170, 1169, 2085], [1637, 1078, 539, 1383], [1457, 14, 1463, 99]], 'adelic_image': '2184.96.2.?', 'conductor': 49686, 'lmfdb_label': '49686.h2', 'prime': 0}
  • id: 213850
    {'conductor': 49686, 'elladic_image': '7.24.0.1', 'lmfdb_label': '49686.h2', 'modell_image': '7B.6.1', 'prime': 7}
• lmfdb_iso 49686.h does not appear in ec_padic