Elliptic curve data - 61248.ca1

Formats: - HTML - YAML - JSON - 2025-10-29T01:52:57.476395

• 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': '61248cb', 'Clabel': '61248cb4', 'Cnumber': 4, 'abc_quality': 1.0126949228662705, 'absD': 16513820155414315008, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 7656, 'ainvs': [0, 1, 0, -16697473, 26255491967], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 29], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 61248, 'degree': 2985984, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7824963526137201680728182683', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 52, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1963975500122834382625, 62995224591882], 'lmfdb_iso': '61248.ca', 'lmfdb_label': '61248.ca1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -260898, -51312870], 'min_quad_twist_disc': -8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.14', '132.24.0.?', '232.6.0.?', '264.48.0.?', '348.24.0.?', '696.48.0.?', '3828.48.0.?', '7656.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 29], [3, 4, 64], [11, 12, 5568], [29, 30, 2112]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7427755817738022039469700861', 'prec': 100}, 'szpiro_ratio': 5.579937983256007, '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, 1, 0, 0, 0, 4, 0, 1, 0, -1, 0, 4, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 1, 0, 4, -1, 4, -6, -4, 0, 1, 4, -2, 6, 8, -6, 0, -6, -2, -4, 0, -4, 10, 12, 12, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 61248, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '61248.ca', 'trace_hash': 1869151064995491326}
• 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': '0.0038296084812657152537744163210', 'prec': 110}, 'conductor': 61248, 'gens': [], 'heights': [], 'lmfdb_label': '61248.ca1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20510519794120346923131159354', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6918935629416624461636086836692054366', 'prec': 130}, 'tamagawa_product': 72, 'torsion_generators': [[2369, 0, 1]], 'xcoord_integral_points': [2369]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '11': [0, 0], '29': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '61248.ca1'}
• ec_torsion_growth •

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

  
  
  • id: 2937591
    {'degree': 2, 'field': [-58, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 2]}
  • id: 2937592
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [6]}
  • id: 2937593
    {'degree': 4, 'field': [58, 0, -23, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [4]}
  • id: 2937594
    {'degree': 4, 'field': [169, 0, -32, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 6]}
  • id: 2937595
    {'degree': 6, 'field': [2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [6]}
  • id: 2937598
    {'degree': 8, 'field': [27, -90, -161, 70, 128, -2, -25, -2, 1], 'lmfdb_label': '61248.ca1', 'torsion': [12]}
  • id: 2937596
    {'degree': 8, 'field': [999, -522, -8367, -2358, 1726, 274, -99, -2, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 4]}
  • id: 2937597
    {'degree': 8, 'field': [221841, 0, 21988, 0, 1202, 0, 92, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 4]}
  • id: 2937599
    {'degree': 12, 'field': [4, 0, -24, 0, 60, 0, -44, 0, 0, 0, 6, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [3, 6]}
  • id: 2937600
    {'degree': 12, 'field': [1940598, 0, 0, -172756, 0, 0, 8474, 0, 0, -92, 0, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 6]}
  • id: 2937602
    {'degree': 16, 'field': [9, -18312, -344708, -2206424, -5866178, -6932352, -2825952, 928368, 992503, 87040, -91832, -14640, 3930, 600, -92, -8, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 12]}
  • id: 2937603
    {'degree': 16, 'field': [256419649, -268761496, 339821812, -126939952, 28104902, 35268920, -28608, -9608104, 1841495, 381688, -83976, 3688, -190, -224, 52, -8, 1], 'lmfdb_label': '61248.ca1', 'torsion': [2, 12]}
  • id: 2937601
    {'degree': 16, 'field': [39064731904, 0, -20962063232, 0, -1959406592, 0, 166787104, 0, 6834004, 0, -818726, 0, 23161, 0, -260, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [8]}
  • id: 2937604
    {'degree': 18, 'field': [-559136475584, 415950323712, 752551139520, -177884552576, -134677947216, 86798994336, 12007860416, -11028222720, -1337780988, 443765200, 44574672, -833832, 993599, 26526, 18657, -542, 36, 0, 1], 'lmfdb_label': '61248.ca1', 'torsion': [18]}
• 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: 1476815
    {'conductor': 61248, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '61248.ca1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1476816
    {'conductor': 61248, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '61248.ca1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1476817
    {'conductor': 61248, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '61248.ca1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1476818
    {'conductor': 61248, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '61248.ca1', 'prime': 29, '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: 2070118
    {'adelic_gens': [[7645, 12, 7644, 13], [3442, 3, 5253, 7648], [2785, 12, 1398, 73], [309, 1592, 346, 1603], [1, 0, 12, 1], [7646, 7653, 3855, 8], [1, 6, 6, 37], [11, 2, 7606, 7647], [1, 12, 0, 1], [5105, 12, 1282, 73]], 'adelic_image': '7656.96.1.?', 'conductor': 61248, 'lmfdb_label': '61248.ca1', 'prime': 0}
  • id: 258357
    {'conductor': 61248, 'elladic_image': '2.3.0.1', 'lmfdb_label': '61248.ca1', 'modell_image': '2B', 'prime': 2}
  • id: 258358
    {'conductor': 61248, 'elladic_image': '3.4.0.1', 'lmfdb_label': '61248.ca1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 61248.ca does not appear in ec_padic