Elliptic curve data - 304704.fp1

Formats: - HTML - YAML - JSON - 2025-10-02T03:46:56.134943

• 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': '304704fp', 'Clabel': '304704fp1', 'Cnumber': 1, 'abc_quality': 0.9705247023922623, 'absD': 36302937943630058496, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [0, 0, 0, -3796104, 2831990920], 'analytic_rank': 1, 'bad_primes': [2, 3, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 304704, 'degree': 6782976, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5926212163011793320916155526', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 145, 'isogeny_degrees': [1, 2], 'jinv': [4499456, 27], 'lmfdb_iso': '304704.fp', 'lmfdb_label': '304704.fp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -199, 1144], 'min_quad_twist_disc': 552, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.f.1', '92.6.0.?', '138.6.0.?', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '25.781535805477363230668931032', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 207], [3, 6, 33856], [23, 156, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.88592824044635887289209845760', 'prec': 107}, 'szpiro_ratio': 4.519016892028105, '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, 0, 0, -2, 0, 0, 0, 6, 0, -2, 0], 'aplist': [0, 0, 2, 2, 0, -2, 6, -2, 0, -6, 0, -4, -2, 6, 4, 6, 0, 4, 10, -8, -10, -10, -16, -6, 4], 'class_deg': 2, 'class_size': 2, 'conductor': 304704, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '304704.fp', 'trace_hash': 466689562598091100}
• 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': '0.0055985791726526397896453190029', 'prec': 110}, 'conductor': 304704, 'gens': [[1036715887682, 798855687806602680, 20381]], 'heights': [{'__RealLiteral__': 0, 'data': '25.781535805477363230668931032', 'prec': 100}], 'lmfdb_label': '304704.fp1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.20697401482900191329562818765', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.672215948234631128856070524696052424', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[1058, 0, 1]], 'xcoord_integral_points': [1058]}
• lmfdb_label 304704.fp1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12877133
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '304704.fp1', 'torsion': [2, 2]}
  • id: 12877134
    {'degree': 4, 'field': [1104, 0, 46, 0, 1], 'lmfdb_label': '304704.fp1', 'torsion': [4]}
  • id: 12877137
    {'degree': 8, 'field': [-192027, 0, 19044, 0, 690, 0, -46, 0, 1], 'lmfdb_label': '304704.fp1', 'torsion': [6]}
  • id: 12877136
    {'degree': 8, 'field': [8464, 0, -4232, 0, 2208, 0, 46, 0, 1], 'lmfdb_label': '304704.fp1', 'torsion': [2, 4]}
  • id: 12877135
    {'degree': 8, 'field': [13225, 0, 4232, 0, -2553, 0, -46, 0, 1], 'lmfdb_label': '304704.fp1', 'torsion': [2, 4]}
  • id: 12877138
    {'degree': 16, 'field': [12924393, 30921360, 35922520, 29508044, 19680014, 10603324, 4849332, 1889072, 605602, 161192, 31860, 3172, -210, -244, -48, 0, 1], 'lmfdb_label': '304704.fp1', 'torsion': [8]}
  • id: 12877139
    {'degree': 16, 'field': [33860761, 0, -161748098, 0, 249837178, 0, 23822986, 0, -878669, 0, -108974, 0, -1610, 0, 46, 0, 1], 'lmfdb_label': '304704.fp1', '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: 7545842
    {'conductor': 304704, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '304704.fp1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7545843
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '304704.fp1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7545844
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '304704.fp1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 3578922
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [112, 1, 179, 0], [1, 2, 2, 5], [1, 4, 0, 1], [94, 1, 91, 0], [273, 4, 272, 5], [209, 70, 68, 207]], 'adelic_image': '276.12.0.?', 'conductor': 304704, 'lmfdb_label': '304704.fp1', 'prime': 0}
  • id: 1072311
    {'conductor': 304704, 'elladic_image': '2.3.0.1', 'lmfdb_label': '304704.fp1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 304704.fp does not appear in ec_padic