Elliptic curve data - 44.a1

Formats: - HTML - YAML - JSON - 2026-05-14T11:46:48.788278

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '44a', 'Clabel': '44a2', 'Cnumber': 2, 'abc_quality': 0.9950617979294879, 'absD': 340736, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 66, 'ainvs': [0, 1, 0, -77, -289], 'analytic_rank': 0, 'bad_primes': [2, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 44, 'degree': 6, 'elladic_images': ['3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10298768145811296210585672847', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-199794688, 1331], 'lmfdb_iso': '44.a', 'lmfdb_label': '44.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -77, -289], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '22.2.0.a.1', '66.16.0-66.a.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 11], [3, 2, 4], [11, 12, 4]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56508580183140983505067814278', 'prec': 107}, 'szpiro_ratio': 6.519077152749634, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, 2, 0, -2, 0, -1, 0, -4, 0, -3, 0, 6, 0, 8, 0], 'aplist': [0, 1, -3, 2, -1, -4, 6, 8, -3, 0, 5, -1, 0, -10, 0, -6, 3, -4, -1, 15, -4, 2, 6, -9, -7], 'class_deg': 3, 'class_size': 2, 'conductor': 44, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '44.a', 'trace_hash': 685433102328794143}
• 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': '1.2287229314726023785377913442', 'prec': 100}, 'conductor': 44, 'gens': [], 'heights': [], 'lmfdb_label': '44.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.80464628757465185995669379233', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.80464628757465185995669379232551592659', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 1], '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '44.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1354
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '44.a1', 'torsion': [3]}
  • id: 1356
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '44.a1', 'torsion': [3]}
  • id: 1355
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '44.a1', 'torsion': [2]}
  • id: 1358
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '44.a1', 'torsion': [3, 3]}
  • id: 1357
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '44.a1', 'torsion': [2, 2]}
  • id: 1359
    {'degree': 6, 'field': [1, 1, 2, -3, 0, -1, 1], 'lmfdb_label': '44.a1', 'torsion': [6]}
  • id: 1360
    {'degree': 9, 'field': [1, 0, 0, 1, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '44.a1', 'torsion': [6]}
  • id: 1361
    {'degree': 12, 'field': [-2, 4, 4, -12, 0, 4, 12, -4, -14, 6, 4, -4, 1], 'lmfdb_label': '44.a1', 'torsion': [4]}
  • id: 1362
    {'degree': 12, 'field': [1, -1, -1, 4, -1, -3, 6, -3, -1, 4, -1, -1, 1], 'lmfdb_label': '44.a1', 'torsion': [2, 6]}
  • id: 1364
    {'degree': 18, 'field': [1, -6, 18, -32, 24, 0, 59, -270, 546, -744, 786, -666, 447, -228, 96, -40, 18, -6, 1], 'lmfdb_label': '44.a1', 'torsion': [3, 6]}
  • id: 1365
    {'degree': 18, 'field': [1, 0, 0, 4, 0, 0, 15, 0, 0, -24, 0, 0, 7, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '44.a1', 'torsion': [2, 6]}
  • id: 1363
    {'degree': 18, 'field': [2197, 0, 0, 2059, 0, 0, 872, 0, 0, -89, 0, 0, -4, 0, 0, -5, 0, 0, 1], 'lmfdb_label': '44.a1', 'torsion': [9]}
• 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: 193
    {'conductor': 44, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '44.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 194
    {'conductor': 44, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '44.a1', '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: 1665976
    {'adelic_gens': [[4, 3, 9, 7], [61, 6, 60, 7], [1, 6, 0, 1], [1, 0, 6, 1], [13, 6, 39, 19], [3, 4, 8, 11], [14, 57, 43, 7]], 'adelic_image': '66.16.0.?', 'conductor': 44, 'lmfdb_label': '44.a1', 'prime': 0}
  • id: 114
    {'conductor': 44, 'elladic_image': '3.8.0.2', 'lmfdb_label': '44.a1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 44.a does not appear in ec_padic