Elliptic curve data - 103056.o2

Formats: - HTML - YAML - JSON - 2024-05-01T15:44:54.612699

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '103056u', 'Clabel': '103056u2', 'Cnumber': 2, 'abc_quality': 0.9802875279667087, 'absD': 918408574895350874112, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 51528, 'ainvs': [0, -1, 0, -6931912, 7176733168], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 113], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 103056, 'degree': 5225472, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8069882443242965086394172679', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2], 'jinv': [-8993380100968273380553, 224220843480310272], 'lmfdb_iso': '103056.o', 'lmfdb_label': '103056.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -433245, -112136456], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '25764.6.0.?', '51528.12.0.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1138410637643511992221851464', 'prec': 100}, 'szpiro_ratio': 5.103576179240312, '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, 2, 0, 0, 0, 1, 0, 4, 0, 4, 0, -2, 0, -2, 0, 1, 0], 'aplist': [0, -1, 2, 0, 4, 4, -2, 1, 8, 8, 10, -2, 6, -12, 0, -2, 0, -6, 4, 2, 10, 16, -16, 10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 103056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '103056.o', 'trace_hash': 755074531144816679}
• 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': '0.0036465400639195543941210069522', 'prec': 110}, 'conductor': 103056, 'gens': [], 'heights': [], 'lmfdb_label': '103056.o2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15699807915365492180314830426', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7679538996877181232755593022153110983', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-3047, 0, 1]], 'xcoord_integral_points': [-3047]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '19': [1, 0], '113': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '103056.o2'}
• ec_torsion_growth •

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

  
  
  • id: 4773168
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [2, 2]}
  • id: 4773169
    {'degree': 4, 'field': [-1568, 0, -13, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [4]}
  • id: 4773172
    {'degree': 8, 'field': [-12, 0, 25, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [6]}
  • id: 4773171
    {'degree': 8, 'field': [558009, 0, 87012, 0, 4884, 0, 116, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [2, 4]}
  • id: 4773170
    {'degree': 8, 'field': [2365444, 0, 79212, 0, -2995, 0, -18, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [2, 4]}
  • id: 4773174
    {'degree': 16, 'field': [8836, 0, 23788, 0, 10369, 0, 6264, 0, 1572, 0, 594, 0, 88, 0, 16, 0, 1], 'lmfdb_label': '103056.o2', 'torsion': [2, 6]}
  • id: 4773173
    {'degree': 16, 'field': [6188990927619600, 0, -13832388927072, 0, -8685613027164, 0, 85739661096, 0, 2828575444, 0, -52488800, 0, 320937, 0, -974, 0, 1], 'lmfdb_label': '103056.o2', '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: 2530774
    {'conductor': 103056, 'conductor_valuation': 4, 'discriminant_valuation': 21, 'j_denominator_valuation': 9, 'kodaira_symbol': -17, 'lmfdb_label': '103056.o2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2530775
    {'conductor': 103056, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '103056.o2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2530776
    {'conductor': 103056, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '103056.o2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 2530777
    {'conductor': 103056, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '103056.o2', 'prime': 113, '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: 2340654
    {'adelic_gens': [[51525, 4, 51524, 5], [17177, 4, 34354, 9], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 25763, 0], [19324, 32209, 6441, 45088], [1, 0, 4, 1], [25993, 4, 458, 9], [3, 4, 8, 11], [40681, 4, 29834, 9]], 'adelic_image': '51528.12.0.?', 'conductor': 103056, 'lmfdb_label': '103056.o2', 'prime': 0}
  • id: 412741
    {'conductor': 103056, 'elladic_image': '8.6.0.5', 'lmfdb_label': '103056.o2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 103056.o does not appear in ec_padic