Elliptic curve data - 315.b2

Formats: - HTML - YAML - JSON - 2026-03-15T06:20:02.196154

• 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': '315a1', 'Cnumber': 1, 'abc_quality': 0.8871538351825968, 'absD': 25515, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 630, 'ainvs': [0, 0, 1, -12, -18], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 315, 'degree': 20, 'elladic_images': ['9.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.42184402070305011138995471682', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-262144, 35], 'lmfdb_iso': '315.b', 'lmfdb_label': '315.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -1, 0], 'min_quad_twist_disc': -3, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '9.24.0-9.a.1.1', '63.72.0-63.e.1.1', '70.2.0.a.1', '210.16.0.?', '630.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 35], [5, 6, 63], [7, 8, 45]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.97115016503710495708757733528', 'prec': 107}, 'szpiro_ratio': 3.350834101485778, '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, 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': '2.3249256066929760911709024605', 'prec': 100}, 'conductor': 315, 'gens': [], 'heights': [], 'lmfdb_label': '315.b2', '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': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• 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.b2'}
• ec_torsion_growth •

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

  
  
  • id: 13166
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '315.b2', 'torsion': [3]}
  • id: 13168
    {'degree': 3, 'field': [-35, 0, 0, 1], 'lmfdb_label': '315.b2', 'torsion': [3]}
  • id: 13167
    {'degree': 3, 'field': [-2, 2, 0, 1], 'lmfdb_label': '315.b2', 'torsion': [2]}
  • id: 13169
    {'degree': 6, 'field': [1, -3, 8, -11, 8, -3, 1], 'lmfdb_label': '315.b2', 'torsion': [2, 2]}
  • id: 13171
    {'degree': 6, 'field': [1, -2, 5, 0, 3, -1, 1], 'lmfdb_label': '315.b2', 'torsion': [9]}
  • id: 13173
    {'degree': 6, 'field': [4, 4, 4, -4, -2, 0, 1], 'lmfdb_label': '315.b2', 'torsion': [6]}
  • id: 13172
    {'degree': 6, 'field': [19, -11, 26, -6, 9, -1, 1], 'lmfdb_label': '315.b2', 'torsion': [9]}
  • id: 13170
    {'degree': 6, 'field': [48, 0, -23, 0, 1, 0, 1], 'lmfdb_label': '315.b2', 'torsion': [3, 3]}
  • id: 13174
    {'degree': 9, 'field': [-62, 204, -208, 21, 63, -14, -7, 4, -3, 1], 'lmfdb_label': '315.b2', 'torsion': [6]}
  • id: 13175
    {'degree': 12, 'field': [-2627, 6158, -5044, -46, 2747, -1660, 72, 332, -161, 22, 12, -6, 1], 'lmfdb_label': '315.b2', 'torsion': [4]}
  • id: 13176
    {'degree': 12, 'field': [1, -3, 1, -2, 23, -43, 50, -43, 23, -2, 1, -3, 1], 'lmfdb_label': '315.b2', 'torsion': [2, 6]}
  • id: 13180
    {'degree': 18, 'field': [1, -14, 90, -336, 769, -1052, 759, -204, 127, -294, 72, 196, -86, -82, 69, -16, 5, -4, 1], 'lmfdb_label': '315.b2', 'torsion': [18]}
  • id: 13179
    {'degree': 18, 'field': [1, -5, 14, -11, -21, 55, 19, -196, 441, -597, 568, -372, 246, -145, 76, -30, 9, -4, 1], 'lmfdb_label': '315.b2', 'torsion': [18]}
  • id: 13177
    {'degree': 18, 'field': [1, -3, 13, -38, 35, 87, -215, -61, 935, -1903, 2255, -1909, 1291, -735, 353, -140, 43, -9, 1], 'lmfdb_label': '315.b2', 'torsion': [3, 9]}
  • id: 13181
    {'degree': 18, 'field': [540, -1440, 4800, 7220, -3430, -4480, 11299, 16079, -3583, -9030, -755, 959, 764, 77, -105, -30, 17, -3, 1], 'lmfdb_label': '315.b2', 'torsion': [2, 6]}
  • id: 13178
    {'degree': 18, 'field': [3844, -12648, 28720, -39828, 42886, -29204, 17269, -6177, 4253, -1908, 1597, -677, 336, -49, 9, 2, 5, -3, 1], 'lmfdb_label': '315.b2', 'torsion': [3, 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: 2920
    {'conductor': 315, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '315.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2921
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '315.b2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2922
    {'conductor': 315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '315.b2', 'prime': 7, '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: 1667076
    {'adelic_gens': [[1, 18, 0, 1], [619, 612, 162, 125], [1, 0, 18, 1], [10, 9, 81, 73], [613, 18, 612, 19], [193, 18, 99, 511], [127, 18, 513, 163], [1, 18, 10, 181]], 'adelic_image': '630.144.3.?', 'conductor': 315, 'lmfdb_label': '315.b2', 'prime': 0}
  • id: 1280
    {'conductor': 315, 'elladic_image': '9.24.0.3', 'lmfdb_label': '315.b2', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 315.b does not appear in ec_padic