Elliptic curve data - 120.a1

Formats: - HTML - YAML - JSON - 2025-04-06T18:00:22.475223

• 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': '120b3', 'Cnumber': 3, 'abc_quality': 0.9916872007915092, 'absD': 829440, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -216, -1296], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 120, 'degree': 32, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.069403084809978099734125542129', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [546718898, 405], 'lmfdb_iso': '120.a', 'lmfdb_label': '120.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -216, -1296], '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.1.3', '20.12.0-4.c.1.1', '24.24.0-24.y.1.8', '40.24.0-40.v.1.4', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 5], [3, 4, 40], [5, 6, 24]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56598183070330510056500390254', 'prec': 107}, 'szpiro_ratio': 5.795114813233983, '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': '0.87039672143611627727395977556', 'prec': 103}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2449101455494914029681337552', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2449101455494914029681337551638236476', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-9, 0, 1]], 'xcoord_integral_points': [-9]}
• 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.a1'}
• ec_torsion_growth •

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

  
  
  • id: 4589
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 2]}
  • id: 4591
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [4]}
  • id: 4590
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [4]}
  • id: 4592
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 4]}
  • id: 4596
    {'degree': 8, 'field': [-48, 0, -16, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [6]}
  • id: 4594
    {'degree': 8, 'field': [6, 0, 52, 0, 9, -10, 3, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [8]}
  • id: 4593
    {'degree': 8, 'field': [31, 164, -178, 32, -25, 8, 2, -4, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 4]}
  • id: 4595
    {'degree': 8, 'field': [100, 0, 80, 0, 54, 0, 8, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [8]}
  • id: 4599
    {'degree': 16, 'field': [36, 0, -96, 0, 340, 0, -204, 0, -51, 0, 46, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 8]}
  • id: 4598
    {'degree': 16, 'field': [81, 0, 108, 0, -108, 0, 408, 0, 823, 0, -136, 0, -12, 0, -4, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 8]}
  • id: 4597
    {'degree': 16, 'field': [625, 0, 0, 0, 0, 0, 0, 0, 850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [4, 4]}
  • id: 4602
    {'degree': 16, 'field': [729, 0, 1944, 0, -540, 0, 1508, 0, -130, 0, 8, 0, 40, 0, 4, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [12]}
  • id: 4600
    {'degree': 16, 'field': [51984, 0, -327744, 0, 249120, 0, -47152, 0, -7000, 0, -1792, 0, 172, 0, -20, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [2, 6]}
  • id: 4601
    {'degree': 16, 'field': [59049, 0, -17496, 0, 0, 0, -3888, 0, 3390, 0, -88, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '120.a1', 'torsion': [12]}
• 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: 823
    {'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '120.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 824
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '120.a1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 825
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '120.a1', '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: 1666244
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [113, 8, 112, 9], [56, 3, 5, 2], [7, 6, 114, 115], [41, 8, 44, 33], [1, 4, 4, 17], [83, 76, 2, 21], [48, 113, 67, 54]], 'adelic_image': '120.48.0.?', 'conductor': 120, 'lmfdb_label': '120.a1', 'prime': 0}
  • id: 432
    {'conductor': 120, 'elladic_image': '8.12.0.7', 'lmfdb_label': '120.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 120.a does not appear in ec_padic