Elliptic curve data - 315.b3

Formats: - HTML - YAML - JSON - 2026-03-06T01:00:24.998696

• 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': '315a', 'Clabel': '315a2', 'Cnumber': 2, 'abc_quality': 1.0649344898971125, 'absD': 31255875, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 630, 'ainvs': [0, 0, 1, 78, 45], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 315, 'degree': 60, 'elladic_images': ['3.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.12746212363100473430766790164', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [71991296, 42875], 'lmfdb_iso': '315.b', 'lmfdb_label': '315.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 9, 1], 'min_quad_twist_disc': -3, 'modell_images': ['3Cs.1.1'], 'modm_images': ['3.24.0-3.a.1.1', '63.72.0-63.b.1.1', '70.2.0.a.1', '210.48.1.?', '630.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 1], [5, 6, 63], [7, 8, 45]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42184402070305011138995471682', 'prec': 107}, 'szpiro_ratio': 4.29090270780684, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -2, 1, 0, 1, 0, 0, 0, 3, 0, 5, 0, 0, 4, -3, 0, 2, -2], 'aplist': [0, 0, 1, 1, 3, 5, -3, 2, 6, -3, -4, 2, 12, -10, -9, -12, 0, 8, -4, 0, 2, -1, -12, 12, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 315, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '315.b', 'trace_hash': 67422632030211171}
• 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': '0.77497520223099203039030082017', 'prec': 103}, 'conductor': 315, 'gens': [], 'heights': [], 'lmfdb_label': '315.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2730829063823660427179612382', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2730829063823660427179612382129197993', 'prec': 130}, 'tamagawa_product': 9, 'torsion_generators': [[3, 17, 1]], 'xcoord_integral_points': [3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 5, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '315.b3'}
• ec_torsion_growth •

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

  
  
  • id: 13182
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '315.b3', 'torsion': [3, 3]}
  • id: 13183
    {'degree': 3, 'field': [-2, 2, 0, 1], 'lmfdb_label': '315.b3', 'torsion': [6]}
  • id: 13184
    {'degree': 6, 'field': [1, -3, 8, -11, 8, -3, 1], 'lmfdb_label': '315.b3', 'torsion': [2, 6]}
  • id: 13185
    {'degree': 6, 'field': [4, 4, 4, -4, -2, 0, 1], 'lmfdb_label': '315.b3', 'torsion': [3, 6]}
  • id: 13186
    {'degree': 9, 'field': [-3465, -5355, -2835, -134, 630, 243, -35, -27, 0, 1], 'lmfdb_label': '315.b3', 'torsion': [9]}
  • id: 13187
    {'degree': 12, 'field': [-2627, 6158, -5044, -46, 2747, -1660, 72, 332, -161, 22, 12, -6, 1], 'lmfdb_label': '315.b3', 'torsion': [12]}
  • id: 13188
    {'degree': 12, 'field': [1, -3, 1, -2, 23, -43, 50, -43, 23, -2, 1, -3, 1], 'lmfdb_label': '315.b3', 'torsion': [6, 6]}
  • id: 13189
    {'degree': 18, 'field': [1, 0, 0, 14, 0, 0, 130, 0, 0, 40, 0, 0, -5, 0, 0, -6, 0, 0, 1], 'lmfdb_label': '315.b3', 'torsion': [3, 9]}
  • id: 13191
    {'degree': 18, 'field': [7, 21, 21, 36, 48, 30, 25, -6, 30, -73, 99, -138, 151, -132, 114, -80, 36, -9, 1], 'lmfdb_label': '315.b3', 'torsion': [3, 9]}
  • id: 13190
    {'degree': 18, 'field': [19683, 0, 0, -25515, 0, 0, 18252, 0, 0, -5355, 0, 0, 676, 0, 0, -35, 0, 0, 1], 'lmfdb_label': '315.b3', 'torsion': [3, 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: 2923
    {'conductor': 315, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '315.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2924
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '315.b3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2925
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '315.b3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1667077
    {'adelic_gens': [[544, 9, 351, 610], [613, 18, 612, 19], [1, 18, 0, 1], [619, 612, 162, 125], [1, 9, 9, 82], [1, 6, 6, 37], [1, 0, 18, 1], [10, 9, 117, 622], [1, 12, 0, 1]], 'adelic_image': '630.144.3.?', 'conductor': 315, 'lmfdb_label': '315.b3', 'prime': 0}
  • id: 1281
    {'conductor': 315, 'elladic_image': '3.24.0.1', 'lmfdb_label': '315.b3', 'modell_image': '3Cs.1.1', 'prime': 3}
• lmfdb_iso 315.b does not appear in ec_padic