Elliptic curve data - 135252.g2

Formats: - HTML - YAML - JSON - 2025-07-17T02:20:56.851320

• 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': '135252e', 'Clabel': '135252e2', 'Cnumber': 2, 'abc_quality': 0.893299145254975, 'absD': 572250158275316541696, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1768, 'ainvs': [0, 0, 0, -3132471, -2424516370], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 135252, 'degree': 4423680, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7098106119513969175586104984', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [-754612278352, 127035441], 'lmfdb_iso': '135252.g', 'lmfdb_label': '135252.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1204, 17876], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '52.12.0.d.1', '104.24.0.?', '136.12.0.?', '1768.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.0320941080885294358841928865', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2601], [3, 8, 15028], [13, 14, 10404], [17, 162, 468]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28179967521593715879139915670', 'prec': 103}, 'szpiro_ratio': 4.8024922292659, '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, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -6, 0], 'aplist': [0, 0, -2, -2, -2, -1, 0, -6, 4, -6, 2, -10, -2, -4, 6, 10, -2, 10, 10, -6, -10, 0, 2, 10, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 135252, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '135252.g', 'trace_hash': 1756185539831467163}
• 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': '0.0044288238627849508675067757347', 'prec': 110}, 'conductor': 135252, 'gens': [[3127, 135486, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.0320941080885294358841928865', 'prec': 100}], 'lmfdb_label': '135252.g2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.056223189274364859866994418518', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3950445538257313681082160256006632151', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[2074, 0, 1]], 'xcoord_integral_points': [2074, 3127]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '135252.g2'}
• ec_torsion_growth •

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

  
  
  • id: 6126859
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '135252.g2', 'torsion': [2, 2]}
  • id: 6126860
    {'degree': 4, 'field': [-2601, 0, -153, 0, 1], 'lmfdb_label': '135252.g2', 'torsion': [4]}
  • id: 6126863
    {'degree': 8, 'field': [-6444, 40752, 21528, 1056, -1248, 30, -17, -2, 1], 'lmfdb_label': '135252.g2', 'torsion': [6]}
  • id: 6126861
    {'degree': 8, 'field': [625, 0, -76, 0, 726, 0, -52, 0, 1], 'lmfdb_label': '135252.g2', 'torsion': [2, 4]}
  • id: 6126862
    {'degree': 8, 'field': [488601, 176148, 31752, 18510, 7639, 410, 2, -2, 1], 'lmfdb_label': '135252.g2', 'torsion': [2, 4]}
  • id: 6126865
    {'degree': 16, 'field': [258064, 0, -1286400, 0, -3265744, 0, -2311920, 0, -515172, 0, 936, 0, 116, 0, -24, 0, 1], 'lmfdb_label': '135252.g2', 'torsion': [8]}
  • id: 6126864
    {'degree': 16, 'field': [12510369, 0, 27729864, 0, 18483426, 0, 3917748, 0, 708319, 0, 68356, 0, 3666, 0, 100, 0, 1], 'lmfdb_label': '135252.g2', 'torsion': [4, 4]}
  • id: 6126866
    {'degree': 16, 'field': [41525136, 0, 1938178368, 0, 393470784, 0, 57075048, 0, 912312, 0, -88812, 0, -2087, 0, 38, 0, 1], 'lmfdb_label': '135252.g2', '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: 3336861
    {'conductor': 135252, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '135252.g2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 3336862
    {'conductor': 135252, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '135252.g2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3336863
    {'conductor': 135252, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '135252.g2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3336864
    {'conductor': 135252, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '135252.g2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2543812
    {'adelic_gens': [[3, 8, 10, 27], [1, 0, 8, 1], [1497, 2, 0, 1], [1, 8, 0, 1], [1761, 8, 1760, 9], [1767, 1760, 1766, 1751], [443, 4, 223, 9], [885, 8, 2, 17], [5, 8, 48, 77], [1663, 1764, 0, 1767]], 'adelic_image': '1768.48.0.?', 'conductor': 135252, 'lmfdb_label': '135252.g2', 'prime': 0}
  • id: 524265
    {'conductor': 135252, 'elladic_image': '4.6.0.5', 'lmfdb_label': '135252.g2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 135252.g does not appear in ec_padic