Elliptic curve data - 120.a4

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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': '120b', 'Clabel': '120b1', 'Cnumber': 1, 'abc_quality': 0.8561074444645796, 'absD': 3840, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, 4, 0], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 120, 'degree': 8, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.62374409574996720968310657933', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [21296, 15], 'lmfdb_iso': '120.a', 'lmfdb_label': '120.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 4, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '12.12.0-4.c.1.2', '20.12.0-4.c.1.2', '24.24.0-24.y.1.2', '30.6.0.a.1', '40.24.0-40.bb.1.9', '60.24.0-60.g.1.4', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 4, 40], [5, 6, 24]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0858422161232640826279279936', 'prec': 103}, 'szpiro_ratio': 3.2399955589480847, '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, -1, 0, 4, 0, 1, 0, 0, 0, -6, 0, -1, 0, -2, 0, 4, 0], 'aplist': [0, 1, -1, 4, 0, -6, -2, 4, -8, -6, 0, -6, 10, -4, 8, 10, 0, 6, -4, 0, -14, 16, 12, 2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '120.a', 'trace_hash': 2081987281515763739}
• 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': '3.4815868857444651090958391022', 'prec': 100}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.4898202910989828059362675103', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2449101455494914029681337551638236476', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '120.a4'}
• ec_torsion_growth •

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

  
  
  • id: 4568
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '120.a4', 'torsion': [4]}
  • id: 4569
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '120.a4', 'torsion': [4]}
  • id: 4567
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '120.a4', 'torsion': [2, 2]}
  • id: 4570
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '120.a4', 'torsion': [2, 4]}
  • id: 4574
    {'degree': 8, 'field': [-48, 0, -16, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [6]}
  • id: 4573
    {'degree': 8, 'field': [4, 24, 44, -24, 6, 0, 2, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [8]}
  • id: 4571
    {'degree': 8, 'field': [16, 0, -28, 0, 24, 0, -7, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [2, 4]}
  • id: 4572
    {'degree': 8, 'field': [36, 0, -8, 0, 24, 0, -12, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [8]}
  • id: 4579
    {'degree': 16, 'field': [-619, 222, -164, 486, 896, -834, -764, 696, 611, -184, -206, 52, 64, -16, -16, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [12]}
  • id: 4575
    {'degree': 16, 'field': [1, -6, 18, -36, 37, 0, -18, 42, -60, 42, -18, 0, 37, -36, 18, -6, 1], 'lmfdb_label': '120.a4', 'torsion': [4, 4]}
  • id: 4580
    {'degree': 16, 'field': [1, -4, 12, -12, 12, -42, 20, 4, 27, 4, 20, -42, 12, -12, 12, -4, 1], 'lmfdb_label': '120.a4', 'torsion': [12]}
  • id: 4577
    {'degree': 16, 'field': [1, 0, 2, 0, -14, 0, 32, 0, 319, 0, 32, 0, -14, 0, 2, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [2, 8]}
  • id: 4576
    {'degree': 16, 'field': [1, 0, 6, 0, 10, 0, 144, 0, 639, 0, 144, 0, 10, 0, 6, 0, 1], 'lmfdb_label': '120.a4', 'torsion': [2, 8]}
  • id: 4578
    {'degree': 16, 'field': [1210, 4620, 434, -7266, 2134, -3684, 8404, -6672, 3443, -1722, 892, -462, 226, -84, 26, -6, 1], 'lmfdb_label': '120.a4', '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: 817
    {'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '120.a4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 818
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '120.a4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 819
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '120.a4', 'prime': 5, '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: 1666247
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [49, 48, 118, 55], [88, 3, 85, 2], [113, 8, 112, 9], [83, 78, 50, 107], [7, 6, 114, 115], [1, 4, 4, 17], [28, 1, 71, 6]], 'adelic_image': '120.48.0.?', 'conductor': 120, 'lmfdb_label': '120.a4', 'prime': 0}
  • id: 435
    {'conductor': 120, 'elladic_image': '8.12.0.12', 'lmfdb_label': '120.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 120.a does not appear in ec_padic