Elliptic curve data - 42978.c2

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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': '42978b', 'Clabel': '42978b2', 'Cnumber': 2, 'abc_quality': 1.0459230879697994, 'absD': 1532291201797601099556, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 57304, 'ainvs': [1, 1, 0, -1003704909, -12239735151735], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 19, 29], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 42978, 'degree': 20459520, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6208959808317576856472894474', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [111825759760338976846738658338393, 1532291201797601099556], 'lmfdb_iso': '42978.c', 'lmfdb_label': '42978.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1003704909, -12239735151735], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '52.12.0-2.a.1.1', '116.12.0.?', '152.12.0.?', '1508.24.0.?', '1976.24.0.?', '4408.24.0.?', '57304.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '30.879359283635622946090328634', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 26], [13, 14, 3306], [19, 20, 2262], [29, 30, 1482]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.6208959808317576856472894474', 'prec': 100}, 'szpiro_ratio': 6.91708155868041, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, -1, 1, 2, 1, 4, -1, 1, -2, -4, -1, 1, -4, -2, 1, 2, -1, -1, 2], 'aplist': [-1, -1, 2, 4, -4, 1, 2, -1, 0, 1, 8, 10, -10, -8, 8, -10, -8, 10, 8, -8, 14, -4, -12, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 42978, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '42978.c', 'trace_hash': 336605986597574019}
• 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': '0.00071602751593622724192228829028', 'prec': 113}, 'conductor': 42978, 'gens': [[1452400630322027, 55016681170082943648278, 67577]], 'heights': [{'__RealLiteral__': 0, 'data': '30.879359283635622946090328634', 'prec': 100}], 'lmfdb_label': '42978.c2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.026822425204736400204185388345', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9695558285329945048582232236516694894', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-18290, 9145, 1], [36582, -18291, 1]], 'xcoord_integral_points': [-18290, 36582]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [1, 0], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [2, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '42978.c2'}
• ec_torsion_growth •

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

  
  
  • id: 2106132
    {'degree': 4, 'field': [16, 0, 21, 0, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 4]}
  • id: 2106131
    {'degree': 4, 'field': [923, 90, -89, -2, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 4]}
  • id: 2106130
    {'degree': 4, 'field': [1719, -70, 71, -2, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 4]}
  • id: 2106133
    {'degree': 8, 'field': [-4, -11, 20, -19, 13, -7, 7, -4, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 6]}
  • id: 2106137
    {'degree': 16, 'field': [81526324, -418877592, 869589436, -982205664, 701675877, -276779758, 132294986, -34070562, 8192590, 245040, -76442, 13794, -1298, -490, 90, -8, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 8]}
  • id: 2106134
    {'degree': 16, 'field': [77409707076, 0, 9160475688, 0, 1031380528, 0, 38005884, 0, 2575205, 0, -10752, 0, 4154, 0, -84, 0, 1], 'lmfdb_label': '42978.c2', 'torsion': [4, 4]}
  • id: 2106135
    {'degree': 16, 'field': [220963561436241, 16130813574408, -15653270337952, -957819962736, 486334587206, -10571305472, 6315421476, -2437171672, 665336231, -38354064, 8668636, -551880, 98350, -2968, 444, -8, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 8]}
  • id: 2106136
    {'degree': 16, 'field': [702484706690017, 1767348588296264, -1766200938494196, -2952522423200, 3135336517854, -2035688280264, 753066067720, -63539443256, 15482451471, 270979064, -56898416, 1469592, -241110, -1792, 276, -8, 1], 'lmfdb_label': '42978.c2', 'torsion': [2, 8]}
• 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: 1020316
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42978.c2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1020317
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42978.c2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1020318
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42978.c2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1020319
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '42978.c2', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1020320
    {'conductor': 42978, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '42978.c2', 'prime': 29, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 1950546
    {'adelic_gens': [[1, 0, 4, 1], [45241, 4, 33178, 9], [57301, 4, 57300, 5], [42981, 4, 28654, 3], [4409, 2, 0, 1], [1, 4, 0, 1], [28653, 4, 2, 9], [15811, 2, 27662, 57303]], 'adelic_image': '57304.48.0.?', 'conductor': 42978, 'lmfdb_label': '42978.c2', 'prime': 0}
  • id: 187437
    {'conductor': 42978, 'elladic_image': '2.6.0.1', 'lmfdb_label': '42978.c2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2139800
    {'lmfdb_iso': '42978.c', 'p': 5, 'prec': 20, 'unit': 1244135170891, 'val': 2}
  • id: 2139786
    {'lmfdb_iso': '42978.c', 'p': 7, 'prec': 20, 'unit': 8277734914127047, 'val': 1}
  • id: 2139784
    {'lmfdb_iso': '42978.c', 'p': 11, 'prec': 20, 'unit': 10116390137544457510, 'val': 1}
  • id: 2139791
    {'lmfdb_iso': '42978.c', 'p': 17, 'prec': 20, 'unit': 112196058499428723962432, 'val': 1}
  • id: 2139787
    {'lmfdb_iso': '42978.c', 'p': 31, 'prec': 20, 'unit': 20508152875299630146939271031, 'val': 1}
  • id: 2139785
    {'lmfdb_iso': '42978.c', 'p': 37, 'prec': 20, 'unit': 406889490534241938007276901233, 'val': 1}
  • id: 2139788
    {'lmfdb_iso': '42978.c', 'p': 41, 'prec': 20, 'unit': 2658083038756980182056217204569, 'val': 1}
  • id: 2139789
    {'lmfdb_iso': '42978.c', 'p': 43, 'prec': 20, 'unit': 3590646874119499884647621769966, 'val': 1}
  • id: 2139798
    {'lmfdb_iso': '42978.c', 'p': 47, 'prec': 20, 'unit': 3282479835878668914489555177086, 'val': 1}
  • id: 2139793
    {'lmfdb_iso': '42978.c', 'p': 53, 'prec': 20, 'unit': 331053349288496526532322121859477, 'val': 1}
  • id: 2139794
    {'lmfdb_iso': '42978.c', 'p': 59, 'prec': 20, 'unit': 2993364851440361104230849390579481, 'val': 1}
  • id: 2139799
    {'lmfdb_iso': '42978.c', 'p': 61, 'prec': 20, 'unit': 4971646944095663850853504120074100, 'val': 1}
  • id: 2139783
    {'lmfdb_iso': '42978.c', 'p': 67, 'prec': 20, 'unit': 1404642007141566117330972660392882, 'val': 1}
  • id: 2139797
    {'lmfdb_iso': '42978.c', 'p': 71, 'prec': 20, 'unit': 120449363466005468729484636307883532, 'val': 1}
  • id: 2139795
    {'lmfdb_iso': '42978.c', 'p': 73, 'prec': 20, 'unit': 85880443259119127292295881220571217, 'val': 1}
  • id: 2139790
    {'lmfdb_iso': '42978.c', 'p': 79, 'prec': 20, 'unit': 38730689739012257134589201502507414, 'val': 1}
  • id: 2139792
    {'lmfdb_iso': '42978.c', 'p': 83, 'prec': 20, 'unit': 1267036204440048738275131109493956836, 'val': 1}
  • id: 2139796
    {'lmfdb_iso': '42978.c', 'p': 89, 'prec': 20, 'unit': 8838906220714186529533846814408529001, 'val': 1}
  • id: 2139782
    {'lmfdb_iso': '42978.c', 'p': 97, 'prec': 20, 'unit': 53515417463167170168440596614503129399, 'val': 1}