Elliptic curve data - 51425.r1

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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
  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': '51425c', 'Clabel': '51425c1', 'Cnumber': 1, 'abc_quality': 0.9072219820005657, 'absD': 102175046875, 'adelic_genus': 3, 'adelic_index': 72, 'adelic_level': 3366, 'ainvs': [0, 1, 1, 917, 11369], 'analytic_rank': 2, 'bad_primes': [5, 11, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 51425, 'degree': 51840, 'elladic_images': ['9.18.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79869937110379647141782984088', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1], 'jinv': [4096000, 4913], 'lmfdb_iso': '51425.r', 'lmfdb_label': '51425.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, 37, 76], 'min_quad_twist_disc': 5, 'modell_images': ['3Ns'], 'modm_images': ['3.6.0.b.1', '9.18.0.a.1', '33.12.0.a.1', '99.36.0.?', '102.12.0.?', '306.36.1.?', '374.2.0.?', '1122.24.1.?', '3366.72.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 12, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.71100242734611694363422294249', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 4675], [3, 2, 3025], [5, 14, 2057], [11, 42, 425], [17, 18, 3025]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.60549340331284635189803572023', 'prec': 107}, 'szpiro_ratio': 2.963342902029106, '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, -2, -2, 0, 0, 3, 0, 1, 0, 0, 4, -6, 0, 0, 4, 1, 0, -6, 0], 'aplist': [0, -2, 0, 3, 0, -6, 1, -6, -6, -9, 4, 2, -9, 6, -3, 3, 9, -6, 5, -12, 9, 0, 0, -15, -8], 'class_deg': 1, 'class_size': 1, 'conductor': 51425, 'isogeny_matrix': [[1]], 'lmfdb_iso': '51425.r', 'trace_hash': 955825952125947111}
• 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': '0.20242238654865985797512870168', 'prec': 103}, 'conductor': 51425, 'gens': [[23, 212, 1], [73, 687, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.42038677932252514016322234883', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.7318568885507468241568799765', 'prec': 100}], 'lmfdb_label': '51425.r1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.71017914172923699906931033794', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0592691234408342059749064835388238775', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [-11, 23, 73, 227, 359, 5497]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 4, 0], '3': [6, 0], '5': 'a', '7': [2, 0], '11': 'a', '13': [2, 0], '17': [3, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '51425.r1'}
• ec_torsion_growth •

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

  
  
  • id: 2492868
    {'degree': 3, 'field': [5, 1, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [2]}
  • id: 2492870
    {'degree': 4, 'field': [-51, 57, 10, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [3]}
  • id: 2492869
    {'degree': 4, 'field': [59, 13, -12, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [3]}
  • id: 2492871
    {'degree': 6, 'field': [383, -219, 56, -51, 18, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [2, 2]}
  • id: 2492872
    {'degree': 8, 'field': [3481, 767, 877, -38, 98, -14, 13, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [3, 3]}
  • id: 2492873
    {'degree': 12, 'field': [-759439071, -584472024, -114940008, 9260046, 4427927, -1197012, -141664, 82144, 21313, -1288, -108, -2, 1], 'lmfdb_label': '51425.r1', 'torsion': [4]}
  • id: 2492875
    {'degree': 12, 'field': [-141261, 1451115, 441415, 54144, -52949, 20303, 3390, 2853, 545, 18, 27, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [6]}
  • id: 2492874
    {'degree': 12, 'field': [247545, 12255, -140679, -12196, 40881, 4453, -6830, -611, 661, 40, -35, -1, 1], 'lmfdb_label': '51425.r1', 'torsion': [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: 1231186
    {'conductor': 51425, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51425.r1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1231187
    {'conductor': 51425, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '51425.r1', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1231188
    {'conductor': 51425, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '51425.r1', 'prime': 17, '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: 2005983
    {'adelic_gens': [[1, 18, 0, 1], [1507, 3002, 1596, 839], [10, 9, 81, 73], [2179, 18, 2781, 163], [3349, 18, 3348, 19], [11, 10, 1531, 1], [17, 18, 84, 89], [1, 0, 18, 1], [13, 6, 3186, 3283]], 'adelic_image': '3366.72.3.?', 'conductor': 51425, 'lmfdb_label': '51425.r1', 'prime': 0}
  • id: 220348
    {'conductor': 51425, 'elladic_image': '9.18.0.1', 'lmfdb_label': '51425.r1', 'modell_image': '3Ns', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2588064
    {'lmfdb_iso': '51425.r', 'p': 7, 'prec': 20, 'unit': 298756497985872, 'val': 2}
  • id: 2588068
    {'lmfdb_iso': '51425.r', 'p': 13, 'prec': 20, 'unit': 403220725375567760094, 'val': 2}
  • id: 2588070
    {'lmfdb_iso': '51425.r', 'p': 19, 'prec': 20, 'unit': 1724443418205526931576851, 'val': 2}
  • id: 2588073
    {'lmfdb_iso': '51425.r', 'p': 23, 'prec': 20, 'unit': 34707542720903597714587667, 'val': 2}
  • id: 2588067
    {'lmfdb_iso': '51425.r', 'p': 29, 'prec': 20, 'unit': 3018669493302294707985796386, 'val': 2}
  • id: 2588078
    {'lmfdb_iso': '51425.r', 'p': 31, 'prec': 20, 'unit': 18421399858896725491164284114, 'val': 2}
  • id: 2588063
    {'lmfdb_iso': '51425.r', 'p': 37, 'prec': 20, 'unit': 142939887695624757326915424770, 'val': 2}
  • id: 2588065
    {'lmfdb_iso': '51425.r', 'p': 41, 'prec': 20, 'unit': 2185271513916700444914635961495, 'val': 2}
  • id: 2588066
    {'lmfdb_iso': '51425.r', 'p': 43, 'prec': 20, 'unit': 2037497494564454892218976816309, 'val': 2}
  • id: 2588069
    {'lmfdb_iso': '51425.r', 'p': 47, 'prec': 20, 'unit': 48775557411346469924580044317187, 'val': 2}
  • id: 2588071
    {'lmfdb_iso': '51425.r', 'p': 53, 'prec': 20, 'unit': 564654163011270432706465107244451, 'val': 2}
  • id: 2588076
    {'lmfdb_iso': '51425.r', 'p': 59, 'prec': 20, 'unit': 2785959137892722870798321054020534, 'val': 2}
  • id: 2588077
    {'lmfdb_iso': '51425.r', 'p': 61, 'prec': 20, 'unit': 7589560040470972027609912719029641, 'val': 2}
  • id: 2588062
    {'lmfdb_iso': '51425.r', 'p': 67, 'prec': 20, 'unit': 30855410660107989384260994675286399, 'val': 2}
  • id: 2588075
    {'lmfdb_iso': '51425.r', 'p': 71, 'prec': 20, 'unit': 126390769545072780666528228551780807, 'val': 2}
  • id: 2588072
    {'lmfdb_iso': '51425.r', 'p': 73, 'prec': 20, 'unit': 50809584151316680036153260414632295, 'val': 2}
  • id: 2588074
    {'lmfdb_iso': '51425.r', 'p': 89, 'prec': 20, 'unit': 3729379277520685717840034858243245498, 'val': 2}
  • id: 2588061
    {'lmfdb_iso': '51425.r', 'p': 97, 'prec': 20, 'unit': 46757584950874951541211427982219500640, 'val': 2}