Elliptic curve data - 78033.c1

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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': '78033c', 'Clabel': '78033c2', 'Cnumber': 2, 'abc_quality': 1.0683303788164564, 'absD': 57176933360386419, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 7030, 'ainvs': [0, 1, 1, -6010366, -5673535913], 'analytic_rank': 1, 'bad_primes': [3, 19, 37], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 78033, 'degree': 2980800, 'elladic_images': ['5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4568662075505407097477912659', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 2, 'isogeny_degrees': [1, 5], 'jinv': [-9358714467168256, 22284891], 'lmfdb_iso': '78033.c', 'lmfdb_label': '78033.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -4390, -113432], 'min_quad_twist_disc': 37, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '38.2.0.a.1', '185.24.0.?', '190.24.1.?', '7030.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '17.582489972862977140633214098', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 26011], [3, 4, 26011], [5, 2, 4107], [19, 20, 4107], [37, 686, 57]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.65140725122842848756374343039', 'prec': 103}, 'szpiro_ratio': 5.187854564378998, '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, 2, 1, 2, -1, 2, 3, 0, 1, -2, -3, 2, 6, 6, -1, -4, -3, 2, 1, -2], 'aplist': [2, 1, -1, 3, -3, 6, -3, 1, -4, 10, -2, 0, -8, 1, 3, -6, 0, -7, 8, 12, -11, 0, 4, -10, 2], 'class_deg': 5, 'class_size': 2, 'conductor': 78033, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '78033.c', 'trace_hash': 421011338643486626}
• 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': '0.0073450224335388130735028336146', 'prec': 110}, 'conductor': 78033, 'gens': [[2717276753, 141559613158879, 196]], 'heights': [{'__RealLiteral__': 0, 'data': '17.582489972862977140633214098', 'prec': 100}], 'lmfdb_label': '78033.c1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.048210791456609203772005356621', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '16.953315147392388188061551094178556588', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 6, 0], '3': [2, 0], '5': [1, 1], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': 'a', '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '78033.c1'}
• ec_torsion_growth •

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

  
  
  • id: 3682865
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '78033.c1', 'torsion': [2]}
  • id: 3682866
    {'degree': 4, 'field': [451, -46, 46, -1, 1], 'lmfdb_label': '78033.c1', 'torsion': [5]}
  • id: 3682867
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '78033.c1', 'torsion': [2, 2]}
  • id: 3682868
    {'degree': 8, 'field': [-20001, -19719, 16769, -2250, 3, -93, 9, 0, 1], 'lmfdb_label': '78033.c1', 'torsion': [3]}
  • id: 3682869
    {'degree': 10, 'field': [-60393, -29820, 24675, 14340, -4920, -2245, 545, 170, -35, -5, 1], 'lmfdb_label': '78033.c1', 'torsion': [5]}
  • id: 3682870
    {'degree': 12, 'field': [-377817777, 319263300, -309151656, 149378610, -24919239, -499816, 520272, -61592, 3753, -60, -8, -2, 1], 'lmfdb_label': '78033.c1', 'torsion': [4]}
  • id: 3682871
    {'degree': 12, 'field': [47252551, 10176343, 21446510, 1767254, 3229225, 91216, 229777, 772, 8339, -54, 148, -1, 1], 'lmfdb_label': '78033.c1', 'torsion': [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: 1898357
    {'conductor': 78033, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '78033.c1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1898358
    {'conductor': 78033, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '78033.c1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 1898359
    {'conductor': 78033, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78033.c1', 'prime': 37, '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: 2179153
    {'adelic_gens': [[3997, 6660, 1480, 741], [7021, 10, 7020, 11], [6, 13, 6975, 6911], [1, 0, 10, 1], [6291, 6660, 3145, 5181], [1, 10, 0, 1], [4179, 0, 0, 7029]], 'adelic_image': '7030.48.1.?', 'conductor': 78033, 'lmfdb_label': '78033.c1', 'prime': 0}
  • id: 321565
    {'conductor': 78033, 'elladic_image': '5.12.0.2', 'lmfdb_label': '78033.c1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 4018404
    {'lmfdb_iso': '78033.c', 'p': 5, 'prec': 20, 'unit': 36908342556262, 'val': 0}
  • id: 4018405
    {'lmfdb_iso': '78033.c', 'p': 7, 'prec': 20, 'unit': 217744105411487, 'val': 1}
  • id: 4018403
    {'lmfdb_iso': '78033.c', 'p': 11, 'prec': 20, 'unit': 11567589263634707454, 'val': 1}
  • id: 4018409
    {'lmfdb_iso': '78033.c', 'p': 13, 'prec': 20, 'unit': 541000368464392942487, 'val': 1}
  • id: 4018411
    {'lmfdb_iso': '78033.c', 'p': 17, 'prec': 20, 'unit': 38498103806115392076080, 'val': 1}
  • id: 4018415
    {'lmfdb_iso': '78033.c', 'p': 23, 'prec': 20, 'unit': 28956628035052632233152619, 'val': 1}
  • id: 4018408
    {'lmfdb_iso': '78033.c', 'p': 29, 'prec': 20, 'unit': 3833363322664555276063161854, 'val': 1}
  • id: 4018419
    {'lmfdb_iso': '78033.c', 'p': 31, 'prec': 20, 'unit': 2131806232305629081118482095, 'val': 1}
  • id: 4018406
    {'lmfdb_iso': '78033.c', 'p': 41, 'prec': 20, 'unit': 739224638334585345614296030584, 'val': 1}
  • id: 4018407
    {'lmfdb_iso': '78033.c', 'p': 43, 'prec': 20, 'unit': 253034984053070416060327399180797, 'val': -1}
  • id: 4018410
    {'lmfdb_iso': '78033.c', 'p': 47, 'prec': 20, 'unit': 31947997528743367275692870964671, 'val': 1}
  • id: 4018413
    {'lmfdb_iso': '78033.c', 'p': 53, 'prec': 20, 'unit': 496629643302923708447841824331985, 'val': 1}
  • id: 4018418
    {'lmfdb_iso': '78033.c', 'p': 61, 'prec': 20, 'unit': 7392677010442086942339360274948525, 'val': 1}
  • id: 4018412
    {'lmfdb_iso': '78033.c', 'p': 67, 'prec': 20, 'unit': 39591709635475756280109175679603040, 'val': 1}
  • id: 4018417
    {'lmfdb_iso': '78033.c', 'p': 71, 'prec': 20, 'unit': 58702793769354205681398179442078250, 'val': 1}
  • id: 4018414
    {'lmfdb_iso': '78033.c', 'p': 73, 'prec': 20, 'unit': 63440932998786655654870323418240498, 'val': 1}
  • id: 4018402
    {'lmfdb_iso': '78033.c', 'p': 83, 'prec': 20, 'unit': 2478377468315738859193266707119898407, 'val': 1}
  • id: 4018416
    {'lmfdb_iso': '78033.c', 'p': 89, 'prec': 20, 'unit': 1000781917750647770266020348574895024, 'val': 1}
  • id: 4018401
    {'lmfdb_iso': '78033.c', 'p': 97, 'prec': 20, 'unit': 43287237832086580017959530824212608613, 'val': 1}