Elliptic curve data - 77.b1

Formats: - HTML - YAML - JSON - 2023-12-11T22:20:14.190413

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '77b', 'Clabel': '77b3', 'Cnumber': 3, 'absD': 539, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 1386, 'ainvs': [0, 1, 1, -89, 295], 'analytic_rank': 0, 'bad_primes': [7, 11], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 77, 'degree': 60, 'elladic_images': ['9.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.29499966938540413647508105321', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-78843215872, 539], 'lmfdb_iso': '77.b', 'lmfdb_label': '77.b1', 'lmfdb_number': 1, 'manin_constant': 3, 'min_quad_twist_ainvs': [0, 1, 1, -89, 295], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '9.24.0-9.a.1.2', '22.2.0.a.1', '63.72.0-63.e.1.2', '66.16.0-66.a.1.4', '198.48.1.?', '1386.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.29499966938540413647508105321', 'prec': 107}, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -2, 3, 0, 1, 0, -2, 0, -1, -2, -4, 0, 3, 4, -6, 0, 2, -6], 'aplist': [0, 1, 3, 1, -1, -4, -6, 2, 3, -6, 5, 11, 6, 8, 0, -6, -9, -10, 5, 9, 2, -10, 12, -3, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 77, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '77.b', 'trace_hash': 874065559975919228}
• 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': '1.8039872225484495154111879817', 'prec': 100}, 'conductor': 77, 'gens': [], 'heights': [], 'lmfdb_label': '77.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '4.6467301969045698455666134453', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0326067104232377434592474322907733706', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': [0, 0], '7': [1, 0], '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '77.b1'}
• ec_torsion_growth •

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

  
  
  • id: 2788
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [9]}
  • id: 2787
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [6]}
  • id: 2789
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [2, 6]}
  • id: 2791
    {'degree': 6, 'field': [31, 7, -17, 8, 4, -3, 1], 'lmfdb_label': '77.b1', 'torsion': [9]}
  • id: 2790
    {'degree': 6, 'field': [400, -520, 656, 14, -25, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [3, 3]}
  • id: 2792
    {'degree': 9, 'field': [-1, -2, 7, -9, -3, 14, 4, 3, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [18]}
  • id: 2793
    {'degree': 12, 'field': [-83, -70, 40, -192, 209, -64, -8, 24, -5, -10, 8, -4, 1], 'lmfdb_label': '77.b1', 'torsion': [12]}
  • id: 2797
    {'degree': 18, 'field': [1, -2, 11, -34, 56, -87, 166, -26, 160, 85, 61, 22, 19, -27, 21, -13, 8, -1, 1], 'lmfdb_label': '77.b1', 'torsion': [2, 18]}
  • id: 2794
    {'degree': 18, 'field': [937, -2709, 823, 5418, -8303, 4316, 2512, -7524, 7625, -4080, 949, 311, -438, 196, -30, -5, 5, -3, 1], 'lmfdb_label': '77.b1', 'torsion': [3, 9]}
  • id: 2796
    {'degree': 18, 'field': [93919, 19033, 36967, -22214, 9437, -24345, 13003, -5025, 8916, -6116, 2771, -819, -277, 447, -189, 21, 15, -6, 1], 'lmfdb_label': '77.b1', 'torsion': [18]}
  • id: 2795
    {'degree': 18, 'field': [11941804, -7189000, 9064888, -4181500, 3245586, -1624340, 979359, -459889, 229893, -92552, 37283, -13955, 5604, -1743, 457, -124, 41, -9, 1], 'lmfdb_label': '77.b1', 'torsion': [3, 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: 436
    {'conductor': 77, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '77.b1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 437
    {'conductor': 77, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '77.b1', 'prime': 11, '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: 1666087
    {'adelic_gens': [[11, 18, 1224, 505], [1, 18, 0, 1], [1, 0, 18, 1], [10, 9, 81, 73], [1369, 18, 1368, 19], [1201, 18, 540, 763], [1135, 18, 513, 163], [1, 18, 10, 181]], 'adelic_image': '1386.144.3.?', 'conductor': 77, 'lmfdb_label': '77.b1', 'prime': 0}
  • id: 243
    {'conductor': 77, 'elladic_image': '9.24.0.1', 'lmfdb_label': '77.b1', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 77.b does not appear in ec_padic