Elliptic curve data - 2304.m2

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• 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': '2304a', 'Clabel': '2304a2', 'Cnumber': 2, 'absD': 644972544, 'ainvs': [0, 0, 0, 216, 0], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': -4, 'conductor': 2304, 'degree': 768, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.37986026628950438706569899621', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2], 'jinv': [1728, 1], 'lmfdb_iso': '2304.m', 'lmfdb_label': '2304.m2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 24, 0], 'min_quad_twist_disc': 12, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5230130575907189611334856350', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 2, 256]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3105329259115095182522750833', 'prec': 103}, 'szpiro_ratio': 3.5827948713609414, '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, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -8, 0, 0, 0], 'aplist': [0, 0, 2, 0, 0, -4, -8, 0, 0, -10, 0, -12, 8, 0, 0, 14, 0, -12, 0, 0, 6, 0, 0, 16, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 2304, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '2304.m', 'trace_hash': 304980776588907830}
• 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': '0.46779714280470213726840721134', 'prec': 103}, 'conductor': 2304, 'gens': [[25, 145, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5230130575907189611334856350', 'prec': 100}], 'lmfdb_label': '2304.m2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.96726122924957778674416678756', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4076739407475124029238699904600992021', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0, 25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [3, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [5, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2304.m2'}
• ec_torsion_growth •

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

  
  
  • id: 116571
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [2, 2]}
  • id: 116572
    {'degree': 4, 'field': [-24, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [4]}
  • id: 116575
    {'degree': 8, 'field': [-12, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [6]}
  • id: 116574
    {'degree': 8, 'field': [36, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [2, 4]}
  • id: 116573
    {'degree': 8, 'field': [49, 0, -68, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [2, 4]}
  • id: 116576
    {'degree': 8, 'field': [180, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [10]}
  • id: 116578
    {'degree': 16, 'field': [-8, 128, 288, 32, 96, 288, -192, -32, 108, -144, 24, 0, -4, -8, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [8]}
  • id: 116581
    {'degree': 16, 'field': [9, 0, 0, 0, 36, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [2, 6]}
  • id: 116577
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [4, 4]}
  • id: 116579
    {'degree': 16, 'field': [144, 0, 0, 0, -144, 0, 0, 0, 156, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [3, 6]}
  • id: 116580
    {'degree': 16, 'field': [1296, 0, 0, 0, -3888, 0, 0, 0, -1476, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [10]}
  • id: 116582
    {'degree': 16, 'field': [2025, 0, 0, 0, 1620, 0, 0, 0, 414, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2304.m2', 'torsion': [2, 10]}
• 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: 38611
    {'conductor': 2304, 'conductor_valuation': 8, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2304.m2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 38612
    {'conductor': 2304, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2304.m2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• lmfdb_label 2304.m2 does not appear in ec_galrep
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 69324
    {'lmfdb_iso': '2304.m', 'p': 5, 'prec': 20, 'unit': 12521843579552, 'val': 1}
  • id: 69317
    {'lmfdb_iso': '2304.m', 'p': 13, 'prec': 20, 'unit': 31762662046145543099, 'val': 1}
  • id: 69319
    {'lmfdb_iso': '2304.m', 'p': 17, 'prec': 20, 'unit': 182734547442847390461441, 'val': 1}
  • id: 69318
    {'lmfdb_iso': '2304.m', 'p': 29, 'prec': 20, 'unit': 1846072191238642990052722634, 'val': 1}
  • id: 69315
    {'lmfdb_iso': '2304.m', 'p': 37, 'prec': 20, 'unit': 155148561728365314949000114210, 'val': 1}
  • id: 69316
    {'lmfdb_iso': '2304.m', 'p': 41, 'prec': 20, 'unit': 810320995083055725009519446058, 'val': 1}
  • id: 69320
    {'lmfdb_iso': '2304.m', 'p': 53, 'prec': 20, 'unit': 59746172631143585335726579153500, 'val': 1}
  • id: 69323
    {'lmfdb_iso': '2304.m', 'p': 61, 'prec': 20, 'unit': 1961194402725659255649230743493320, 'val': 1}
  • id: 69321
    {'lmfdb_iso': '2304.m', 'p': 73, 'prec': 20, 'unit': 221801908321535062546657993434876183, 'val': 1}
  • id: 69322
    {'lmfdb_iso': '2304.m', 'p': 89, 'prec': 20, 'unit': 2949196517930383732080845741961800912, 'val': 1}
  • id: 69314
    {'lmfdb_iso': '2304.m', 'p': 97, 'prec': 20, 'unit': 19105871608783254123090627631341892199, 'val': 1}