Elliptic curve data - 5819.a3

Formats: - HTML - YAML - JSON - 2026-01-24T05:03:25.009338

• 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': '5819a', 'Clabel': '5819a1', 'Cnumber': 1, 'abc_quality': 0.8254556483942886, 'absD': 1628394779, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 12650, 'ainvs': [0, -1, 1, -176, -2082], 'analytic_rank': 0, 'bad_primes': [11, 23], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 5819, 'degree': 2530, 'elladic_images': ['25.60.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.45501831062912159341398248783', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-4096, 11], 'lmfdb_iso': '5819.a', 'lmfdb_label': '5819.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, 0, 0], 'min_quad_twist_disc': -23, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '22.2.0.a.1', '25.60.0.a.1', '110.24.1.?', '115.24.0.?', '275.300.12.?', '550.600.37.?', '575.120.0.?', '2530.48.1.?', '6325.600.12.?', '12650.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[11, 12, 529], [23, 266, 11]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 103}, 'szpiro_ratio': 3.329232150359142, '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, -2, -1, 2, -1, 2, 2, 0, -2, 2, -1, -2, 4, -4, 1, -4, 2, 4, 0, -2], 'aplist': [-2, -1, -1, 2, -1, 4, 2, 0, 0, 0, 7, -3, -8, 6, 8, 6, 5, -12, 7, -3, 4, 10, 6, -15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 5819, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '5819.a', 'trace_hash': 1670274379053755884}
• 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': '0.40250948335999115602347971996', 'prec': 103}, 'conductor': 5819, 'gens': [], 'heights': [], 'lmfdb_label': '5819.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60836858419530883797686315062', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.60836858419530883797686315061993154818', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 1, 0], '3': [0, 0], '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0, 0], '23': 'a', '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '5819.a3'}
• ec_torsion_growth •

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

  
  
  • id: 302993
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '5819.a3', 'torsion': [5]}
  • id: 302994
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '5819.a3', 'torsion': [2]}
  • id: 302995
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '5819.a3', 'torsion': [2, 2]}
  • id: 302996
    {'degree': 6, 'field': [146, 8, 104, -15, 19, -1, 1], 'lmfdb_label': '5819.a3', 'torsion': [10]}
  • id: 302997
    {'degree': 8, 'field': [-8207, -5780, -2198, 651, -249, 57, -2, -2, 1], 'lmfdb_label': '5819.a3', 'torsion': [3]}
  • id: 302998
    {'degree': 10, 'field': [22793, -5129, 10496, -2373, 2334, -484, 310, -52, 24, -3, 1], 'lmfdb_label': '5819.a3', 'torsion': [25]}
  • id: 302999
    {'degree': 12, 'field': [-5581609, 3012412, 496474, -1071618, 329451, 7480, 5508, 1856, -841, -96, 6, -2, 1], 'lmfdb_label': '5819.a3', 'torsion': [4]}
  • id: 303000
    {'degree': 12, 'field': [46656, -7776, -20736, 8424, 1584, -978, 511, -163, 44, 39, -16, -1, 1], 'lmfdb_label': '5819.a3', 'torsion': [2, 10]}
  • id: 303001
    {'degree': 16, 'field': [1423249, 0, 1540951, 0, 900400, 0, 326571, 0, 73929, 0, 10581, 0, 931, 0, 46, 0, 1], 'lmfdb_label': '5819.a3', 'torsion': [15]}
  • id: 303002
    {'degree': 20, 'field': [391359307120, -201798989320, -197073337760, 82835405380, 56343674751, -15067558982, -10745197080, 1347096085, 1309822655, -59173836, -109341243, -241640, 6474405, 202045, -268018, -11859, 7410, 305, -125, -3, 1], 'lmfdb_label': '5819.a3', 'torsion': [5]}
• 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: 114825
    {'conductor': 5819, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5819.a3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 114826
    {'conductor': 5819, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5819.a3', 'prime': 23, 'reduction_type': 0, '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: 1702021
    {'adelic_gens': [[1, 0, 50, 1], [1099, 0, 0, 12649], [1, 50, 0, 1], [9316, 7705, 3335, 6786], [38, 41, 10091, 9889], [4716, 4945, 9177, 3037], [12601, 50, 12600, 51]], 'adelic_image': '12650.1200.37.?', 'conductor': 5819, 'lmfdb_label': '5819.a3', 'prime': 0}
  • id: 28694
    {'conductor': 5819, 'elladic_image': '25.60.0.1', 'lmfdb_label': '5819.a3', 'modell_image': '5B.4.1', 'prime': 5}
• lmfdb_iso 5819.a does not appear in ec_padic