Elliptic curve data - 7728.o2

Formats: - HTML - YAML - JSON - 2024-04-19T21:40:54.555821

• 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': '7728r', 'Clabel': '7728r3', 'Cnumber': 3, 'abc_quality': 0.9988665037729055, 'absD': 78205013655552, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2576, 'ainvs': [0, 1, 0, -283424, -58169868], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 7728, 'degree': 49152, 'elladic_images': ['8.48.0.176'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7625481433198103661336076428', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [614716917569296417, 19093020912], 'lmfdb_iso': '7728.o', 'lmfdb_label': '7728.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -17714, 900047], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.48.0-8.bb.1.3', '92.24.0.?', '112.96.0.?', '184.96.0.?', '2576.192.1.?'], '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': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0694009627598650567163755213', 'prec': 100}, 'szpiro_ratio': 5.504286445991201, '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, -1, 0, 1, 0, 4, 0, -2, 0, -2, 0, -6, 0, -4, 0], 'aplist': [0, 1, -2, -1, 4, -2, -6, -4, 1, -2, 8, 6, -6, 4, 8, 6, -4, -10, -4, 8, -6, 0, 12, 2, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 7728, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '7728.o', 'trace_hash': 914201361978304918}
• 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': '0.029448971690066153572926995190', 'prec': 107}, 'conductor': 7728, 'gens': [], 'heights': [], 'lmfdb_label': '7728.o2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20691457370622316265645147862', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6553165896497853012516118289840482818', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-309, 0, 1]], 'xcoord_integral_points': [-309]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '7': [0, 0], '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '7728.o2'}
• ec_torsion_growth •

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

  
  
  • id: 404400
    {'degree': 2, 'field': [-23, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 2]}
  • id: 404402
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [8]}
  • id: 404401
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '7728.o2', 'torsion': [4]}
  • id: 404404
    {'degree': 4, 'field': [-207, 0, 0, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 4]}
  • id: 404403
    {'degree': 4, 'field': [36, 0, -11, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 8]}
  • id: 404405
    {'degree': 4, 'field': [828, 0, 0, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [8]}
  • id: 404408
    {'degree': 8, 'field': [-768, 0, -316, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [6]}
  • id: 404406
    {'degree': 8, 'field': [42436, 0, 2488, 0, -408, 0, 4, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [4, 8]}
  • id: 404407
    {'degree': 8, 'field': [42849, 0, 0, 0, 162, 0, 0, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [16]}
  • id: 404411
    {'degree': 16, 'field': [20164, 0, -39848, 0, 63041, 0, -47020, 0, 19040, 0, -4282, 0, 540, 0, -36, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 16]}
  • id: 404409
    {'degree': 16, 'field': [36481, 0, -93760, 0, -114128, 0, -24976, 0, 706, 0, -448, 0, 112, 0, -16, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 8]}
  • id: 404415
    {'degree': 16, 'field': [299209, 0, -188272, 0, 250204, 0, 154824, 0, 19230, 0, -192, 0, -164, 0, 8, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [24]}
  • id: 404410
    {'degree': 16, 'field': [1350244, 0, 2100392, 0, -54512, 0, 7940, 0, 25477, 0, 596, 0, -242, 0, 8, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 16]}
  • id: 404414
    {'degree': 16, 'field': [2415312, -6128784, 9627732, -9431616, 11055456, -8335936, 4033544, -1160176, 401765, -84256, 27332, -6632, 1894, -392, 76, -8, 1], 'lmfdb_label': '7728.o2', 'torsion': [12]}
  • id: 404413
    {'degree': 16, 'field': [39790864, 0, -50955328, 0, 8647552, 0, 362945, 0, -52886, 0, -13543, 0, 865, 0, -46, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [2, 6]}
  • id: 404412
    {'degree': 16, 'field': [10406127420743184, 0, 0, 0, 3009406618368, 0, 0, 0, 704079864, 0, 0, 0, 39744, 0, 0, 0, 1], 'lmfdb_label': '7728.o2', 'torsion': [16]}
• 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: 159558
    {'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '7728.o2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 159559
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7728.o2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 159560
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '7728.o2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 159561
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.o2', 'prime': 23, '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: 1715004
    {'adelic_gens': [[1473, 16, 1480, 129], [1, 16, 0, 1], [1920, 5, 1523, 2562], [15, 2, 2478, 2563], [2561, 16, 2560, 17], [5, 4, 2572, 2573], [1, 0, 16, 1], [958, 637, 1585, 1266], [1, 16, 652, 773]], 'adelic_image': '2576.192.1.?', 'conductor': 7728, 'lmfdb_label': '7728.o2', 'prime': 0}
  • id: 37882
    {'conductor': 7728, 'elladic_image': '8.48.0.176', 'lmfdb_label': '7728.o2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 7728.o does not appear in ec_padic