Elliptic curve data - 196800.gl2

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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': '196800gy', 'Clabel': '196800gy2', 'Cnumber': 2, 'abc_quality': 1.0617280385727412, 'absD': 248913094678707437568000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 328, 'ainvs': [0, 1, 0, -725210433, -7555463776737], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 41], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 196800, 'degree': 82575360, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9053932074337881797514357415', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 167, 'isogeny_degrees': [1, 2], 'jinv': [-10298071306410575356297, 60769798505543808], 'lmfdb_iso': '196800.gl', 'lmfdb_label': '196800.gl2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -453257, -118088116], 'min_quad_twist_disc': 40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '164.6.0.?', '328.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 25], [3, 4, 65600], [5, 14, 7872], [41, 42, 4800]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0609534803768200283252078927', 'prec': 100}, 'szpiro_ratio': 5.97456970592472, '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, 0, 0, -2, 0, 1, 0, -4, 0, 4, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 1, 0, -2, -4, 4, 2, 0, -4, 0, 4, 2, -1, -12, 2, -4, 4, -10, -8, -10, 2, -14, -12, 10, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 196800, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '196800.gl', 'trace_hash': 259902117556727875}
• 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': '0.00040533915770659689305357809302', 'prec': 113}, 'conductor': 196800, 'gens': [], 'heights': [], 'lmfdb_label': '196800.gl2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.014541203449008573260897018861', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3959555311048230330461138106379081508', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[31113, 0, 1]], 'xcoord_integral_points': [31113]}
• lmfdb_label 196800.gl2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8647079
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '196800.gl2', 'torsion': [2, 2]}
  • id: 8647080
    {'degree': 4, 'field': [10, -25, -1, -1, 1], 'lmfdb_label': '196800.gl2', 'torsion': [4]}
  • id: 8647083
    {'degree': 8, 'field': [-7500, 0, -3250, 0, -300, 0, 0, 0, 1], 'lmfdb_label': '196800.gl2', 'torsion': [6]}
  • id: 8647081
    {'degree': 8, 'field': [289, 0, 76, 0, 200, 0, 28, 0, 1], 'lmfdb_label': '196800.gl2', 'torsion': [2, 4]}
  • id: 8647082
    {'degree': 8, 'field': [1314, 312, 421, 214, 97, -60, 7, -2, 1], 'lmfdb_label': '196800.gl2', 'torsion': [2, 4]}
  • id: 8647084
    {'degree': 16, 'field': [-1039086, 2989416, -2769212, -3387248, 4925185, -1676084, 425438, -374660, 217961, -78528, 10664, 1592, 227, -244, 22, -4, 1], 'lmfdb_label': '196800.gl2', 'torsion': [8]}
  • id: 8647085
    {'degree': 16, 'field': [4769856, 0, 34127424, 0, 16359492, 0, 4010192, 0, 285920, 0, -3652, 0, -488, 0, 16, 0, 1], 'lmfdb_label': '196800.gl2', '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: 4874427
    {'conductor': 196800, 'conductor_valuation': 6, 'discriminant_valuation': 25, 'j_denominator_valuation': 7, 'kodaira_symbol': -19, 'lmfdb_label': '196800.gl2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4874428
    {'conductor': 196800, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '196800.gl2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 24}
  • id: 4874429
    {'conductor': 196800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '196800.gl2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4874430
    {'conductor': 196800, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '196800.gl2', 'prime': 41, '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: 2926287
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [325, 4, 324, 5], [124, 209, 41, 288], [1, 2, 2, 5], [1, 4, 0, 1], [129, 4, 258, 9], [2, 1, 163, 0]], 'adelic_image': '328.12.0.?', 'conductor': 196800, 'lmfdb_label': '196800.gl2', 'prime': 0}
  • id: 731302
    {'conductor': 196800, 'elladic_image': '8.6.0.5', 'lmfdb_label': '196800.gl2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 196800.gl does not appear in ec_padic