Elliptic curve data - 9996.g1

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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': '9996e', 'Clabel': '9996e1', 'Cnumber': 1, 'abc_quality': 1.0308336303888312, 'absD': 9592479809305344, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 714, 'ainvs': [0, -1, 0, -146869, -22121903], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 9996, 'degree': 82944, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8478882297544113128090875783', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 3], 'jinv': [-11632923639808, 318495051], 'lmfdb_iso': '9996.g', 'lmfdb_label': '9996.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2997, 63639], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.1', '102.8.0.?', '714.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.1096642308267377187733956329', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2499], [3, 4, 196], [7, 32, 204], [17, 18, 588]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41283503485345778731158979227', 'prec': 103}, 'szpiro_ratio': 5.141371466817552, '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, 3, 0, 0, 0, 1, 0, -3, 0, 1, 0, -3, 0, -1, 0, -5, 0], 'aplist': [0, -1, 3, 0, -3, 1, -1, -5, -3, -6, 10, -4, 9, -1, 6, 6, 6, -8, -4, -12, 10, -10, -6, -12, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 9996, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '9996.g', 'trace_hash': 1620148927214678673}
• 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': '0.024828168109018261115195617511', 'prec': 107}, 'conductor': 9996, 'gens': [[7719, 677278, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.1096642308267377187733956329', 'prec': 100}], 'lmfdb_label': '9996.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12174059027380821739036587286', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4627647790137170573304629700539028340', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [7719]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 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': '9996.g1'}
• ec_torsion_growth •

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

  
  
  • id: 518596
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '9996.g1', 'torsion': [3]}
  • id: 518597
    {'degree': 3, 'field': [-3, 1, -1, 1], 'lmfdb_label': '9996.g1', 'torsion': [2]}
  • id: 518599
    {'degree': 6, 'field': [1, -5, 4, 1, 2, -3, 1], 'lmfdb_label': '9996.g1', 'torsion': [3]}
  • id: 518598
    {'degree': 6, 'field': [9, -27, 30, -15, 4, -1, 1], 'lmfdb_label': '9996.g1', 'torsion': [2, 2]}
  • id: 518600
    {'degree': 6, 'field': [14, -28, 8, 1, 7, -1, 1], 'lmfdb_label': '9996.g1', 'torsion': [6]}
  • id: 518601
    {'degree': 12, 'field': [-120207, -160480, -38042, 63046, 48617, 20896, 5152, 768, 15, -60, -10, -2, 1], 'lmfdb_label': '9996.g1', 'torsion': [4]}
  • id: 518602
    {'degree': 12, 'field': [1, -5, 21, -22, 19, 21, -20, 21, 3, -8, 7, -3, 1], 'lmfdb_label': '9996.g1', 'torsion': [3, 3]}
  • id: 518603
    {'degree': 12, 'field': [373, 1006, 1393, 744, 870, -334, 369, -236, 162, -42, 25, -4, 1], 'lmfdb_label': '9996.g1', 'torsion': [2, 6]}
  • id: 518605
    {'degree': 18, 'field': [-48, -288, -536, 1200, 744, -2730, 4305, -6171, 6045, -3624, 1255, -141, -126, 63, 39, -60, 33, -9, 1], 'lmfdb_label': '9996.g1', 'torsion': [6]}
  • id: 518604
    {'degree': 18, 'field': [359318006023, 18170041377, 218802469440, -6951701564, 51539147361, -3384522507, 6486510306, -471645303, 486026346, -32307081, 23472408, -1311699, 743790, -34395, 15183, -550, 192, -3, 1], 'lmfdb_label': '9996.g1', '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: 211318
    {'conductor': 9996, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '9996.g1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 211319
    {'conductor': 9996, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '9996.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 211320
    {'conductor': 9996, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '9996.g1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 211321
    {'conductor': 9996, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '9996.g1', 'prime': 17, '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: 1730079
    {'adelic_gens': [[3, 4, 8, 11], [4, 3, 9, 7], [1, 0, 6, 1], [120, 91, 343, 36], [547, 210, 315, 631], [305, 0, 0, 713], [709, 6, 708, 7], [1, 6, 0, 1]], 'adelic_image': '714.16.0.?', 'conductor': 9996, 'lmfdb_label': '9996.g1', 'prime': 0}
  • id: 48298
    {'conductor': 9996, 'elladic_image': '3.4.0.1', 'lmfdb_label': '9996.g1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 421779
    {'lmfdb_iso': '9996.g', 'p': 5, 'prec': 20, 'unit': 16610081083944, 'val': 1}
  • id: 421778
    {'lmfdb_iso': '9996.g', 'p': 11, 'prec': 20, 'unit': 17958419322518621894, 'val': 1}
  • id: 421785
    {'lmfdb_iso': '9996.g', 'p': 13, 'prec': 20, 'unit': 15398066370771606624014, 'val': -1}
  • id: 421788
    {'lmfdb_iso': '9996.g', 'p': 19, 'prec': 20, 'unit': 1541830880945996185802398, 'val': 1}
  • id: 421791
    {'lmfdb_iso': '9996.g', 'p': 23, 'prec': 20, 'unit': 56930616717951254701565252, 'val': 1}
  • id: 421784
    {'lmfdb_iso': '9996.g', 'p': 29, 'prec': 20, 'unit': 2758100846169207714456380435, 'val': 1}
  • id: 421781
    {'lmfdb_iso': '9996.g', 'p': 31, 'prec': 20, 'unit': 16744562782195102594354998052, 'val': 1}
  • id: 421796
    {'lmfdb_iso': '9996.g', 'p': 37, 'prec': 20, 'unit': 189863867697778226445370759613, 'val': 1}
  • id: 421782
    {'lmfdb_iso': '9996.g', 'p': 41, 'prec': 20, 'unit': 2282767816186477253678655350196, 'val': 1}
  • id: 421783
    {'lmfdb_iso': '9996.g', 'p': 43, 'prec': 20, 'unit': 8246318407865449640030118625447, 'val': 1}
  • id: 421793
    {'lmfdb_iso': '9996.g', 'p': 47, 'prec': 20, 'unit': 31037040896358812271575666826600, 'val': 1}
  • id: 421789
    {'lmfdb_iso': '9996.g', 'p': 53, 'prec': 20, 'unit': 522999287255288512330561681262369, 'val': 1}
  • id: 421787
    {'lmfdb_iso': '9996.g', 'p': 59, 'prec': 20, 'unit': 729997833028409159172645709659912, 'val': 1}
  • id: 421794
    {'lmfdb_iso': '9996.g', 'p': 61, 'prec': 20, 'unit': 6111495159451054907588772323980757, 'val': 1}
  • id: 421777
    {'lmfdb_iso': '9996.g', 'p': 67, 'prec': 20, 'unit': 36567727549787984959294225573017995, 'val': 1}
  • id: 421780
    {'lmfdb_iso': '9996.g', 'p': 71, 'prec': 20, 'unit': 117633154716492981964372503305969570, 'val': 1}
  • id: 421790
    {'lmfdb_iso': '9996.g', 'p': 73, 'prec': 20, 'unit': 95301578713259552490446965317196817, 'val': 1}
  • id: 421786
    {'lmfdb_iso': '9996.g', 'p': 79, 'prec': 20, 'unit': 4838552588661775574167833735737453, 'val': 2}
  • id: 421795
    {'lmfdb_iso': '9996.g', 'p': 83, 'prec': 20, 'unit': 1714675516048002195302876832938157271, 'val': 1}
  • id: 421792
    {'lmfdb_iso': '9996.g', 'p': 89, 'prec': 20, 'unit': 6767236431393864360487042389054728811, 'val': 1}
  • id: 421776
    {'lmfdb_iso': '9996.g', 'p': 97, 'prec': 20, 'unit': 12829131352933151789179178781292775403, 'val': 1}