Elliptic curve data - 3315.b4

Formats: - HTML - YAML - JSON - 2025-11-06T11:56:36.908024

• 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': '3315e', 'Clabel': '3315e4', 'Cnumber': 4, 'abc_quality': 0.9933257523075025, 'absD': 566398828125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1768, 'ainvs': [1, 0, 0, 124, -36195], 'analytic_rank': 0, 'bad_primes': [3, 5, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3315, 'degree': 4096, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.93416143787672118712883440015', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [210751100351, 566398828125], 'lmfdb_iso': '3315.b', 'lmfdb_label': '3315.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 124, -36195], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '52.12.0-4.c.1.2', '68.12.0-4.c.1.1', '104.24.0.?', '136.24.0.?', '884.24.0.?', '1768.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 221], [3, 4, 1105], [5, 6, 663], [13, 14, 255], [17, 18, 195]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.93416143787672118712883440015', 'prec': 103}, 'szpiro_ratio': 4.2581004621455625, '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, -1, 1, -1, -1, -1, 4, 3, 1, 1, 0, -1, 1, -4, -1, -1, 1, -1, 4, 1], 'aplist': [-1, 1, -1, 4, 0, 1, 1, 4, 8, -2, 4, 2, -2, -4, -8, -10, 12, -2, 4, -4, -2, 8, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 3315, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3315.b', 'trace_hash': 425917676381075106}
• 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': '0.15438236322189234184693327277', 'prec': 103}, 'conductor': 3315, 'gens': [], 'heights': [], 'lmfdb_label': '3315.b4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.42714617749035960929849510246', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7085847099614384371939804098328355584', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[127, -127, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 2], '3': [5, 0], '5': [0, 0], '13': [1, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '3315.b4'}
• ec_torsion_growth •

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

  
  
  • id: 173223
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '3315.b4', 'torsion': [4]}
  • id: 173224
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [4]}
  • id: 173222
    {'degree': 2, 'field': [221, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [2, 2]}
  • id: 173226
    {'degree': 4, 'field': [-221, 0, 13, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [8]}
  • id: 173225
    {'degree': 4, 'field': [417, -28, 29, -2, 1], 'lmfdb_label': '3315.b4', 'torsion': [2, 4]}
  • id: 173230
    {'degree': 8, 'field': [2925, -15588, 15480, 215, -104, -7, 7, -4, 1], 'lmfdb_label': '3315.b4', 'torsion': [6]}
  • id: 173227
    {'degree': 8, 'field': [59926, -11236, 11774, -1060, 491, 44, -10, -4, 1], 'lmfdb_label': '3315.b4', 'torsion': [2, 4]}
  • id: 173229
    {'degree': 8, 'field': [75357, -20556, 18780, -13466, 1699, 22, 58, -2, 1], 'lmfdb_label': '3315.b4', 'torsion': [2, 8]}
  • id: 173228
    {'degree': 8, 'field': [781456, 0, 0, 0, 2057, 0, 0, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [8]}
  • id: 173232
    {'degree': 16, 'field': [21381376, 0, 0, 0, 10612080, 0, 0, 0, 1054561, 0, 0, 0, 2295, 0, 0, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [2, 8]}
  • id: 173235
    {'degree': 16, 'field': [2383880625, 0, -1539374625, 0, 240613200, 0, -8576053, 0, 1378277, 0, 27953, 0, 79, 0, -26, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [12]}
  • id: 173233
    {'degree': 16, 'field': [2385443281, 0, 4490246176, 0, 840651292, 0, -54311192, 0, 2573545, 0, 245752, 0, 17212, 0, -416, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [16]}
  • id: 173236
    {'degree': 16, 'field': [2385443281, 0, 33633670876, 0, 4225332592, 0, 277251283, 0, 9011020, 0, -87023, 0, -2363, 0, 34, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [12]}
  • id: 173231
    {'degree': 16, 'field': [3110627529, 0, -953098664, 0, 119463970, 0, -7437388, 0, 206195, 0, -4060, 0, 1214, 0, 28, 0, 1], 'lmfdb_label': '3315.b4', 'torsion': [4, 4]}
  • id: 173234
    {'degree': 16, 'field': [36020816793, -28489041828, 36693937593, -17403996526, 11233380920, -3166520880, 1271570467, -187843004, 50397657, -2493150, 700557, -110220, 18461, -70, 30, -8, 1], 'lmfdb_label': '3315.b4', '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: 60300
    {'conductor': 3315, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3315.b4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 60301
    {'conductor': 3315, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3315.b4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 60302
    {'conductor': 3315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3315.b4', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 60303
    {'conductor': 3315, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3315.b4', 'prime': 17, '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: 1685566
    {'adelic_gens': [[7, 6, 1762, 1763], [1, 0, 8, 1], [1, 8, 0, 1], [667, 666, 234, 1115], [1761, 8, 1760, 9], [1, 4, 4, 17], [224, 1113, 249, 296], [1368, 3, 413, 2], [420, 1, 647, 6]], 'adelic_image': '1768.48.0.?', 'conductor': 3315, 'lmfdb_label': '3315.b4', 'prime': 0}
  • id: 16644
    {'conductor': 3315, 'elladic_image': '8.12.0.6', 'lmfdb_label': '3315.b4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3315.b does not appear in ec_padic