Elliptic curve data - 4900.a1

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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': '4900o', 'Clabel': '4900o1', 'Cnumber': 1, 'abc_quality': 0.6163775175776384, 'absD': 980000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 20, 'ainvs': [0, 0, 0, -175, 1750], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 4900, 'degree': 3456, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.41613244052656581469069970753', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-3024, 5], 'lmfdb_iso': '4900.a', 'lmfdb_label': '4900.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -7, 14], 'min_quad_twist_disc': 5, 'modell_images': [], 'modm_images': ['20.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.12423808411429927810607327918', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 1225], [5, 18, 196], [7, 14, 100]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1750029942396667964053934973', 'prec': 103}, 'szpiro_ratio': 3.3491725952499736, '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, -3, 0, 0, 0, 0, 0, 6, 0, -2, 0, -6, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, -3, 0, 0, -2, -6, 2, 0, 9, 3, -2, -8, -5, -1, 8, -4, 8, -7, 3, 8, 14, 4, -1, -13, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 4900, 'isogeny_matrix': [[1]], 'lmfdb_iso': '4900.a', 'trace_hash': 207909564428744349}
• 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': '0.43506280410884607583973802559', 'prec': 103}, 'conductor': 4900, 'gens': [[15, 50, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.12423808411429927810607327918', 'prec': 103}], 'lmfdb_label': '4900.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4012560100991859057583273187', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0890723445804406874482315658797497203', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [-10, -5, 11, 15, 415]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': 'a', '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4900.a1'}
• ec_torsion_growth •

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

  
  
  • id: 255929
    {'degree': 3, 'field': [-13, 5, -1, 1], 'lmfdb_label': '4900.a1', 'torsion': [2]}
  • id: 255930
    {'degree': 6, 'field': [20, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '4900.a1', 'torsion': [2, 2]}
  • id: 255931
    {'degree': 8, 'field': [-971, 2345, -1637, 752, -320, 62, 25, -1, 1], 'lmfdb_label': '4900.a1', 'torsion': [3]}
  • id: 255932
    {'degree': 12, 'field': [-2890, -2340, -3690, -2480, -1202, -680, 6, 184, 15, 2, 5, -6, 1], 'lmfdb_label': '4900.a1', 'torsion': [4]}
• 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: 94520
    {'conductor': 4900, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '4900.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 94521
    {'conductor': 4900, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4900.a1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 94522
    {'conductor': 4900, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '4900.a1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'adelic_gens': [[1, 2, 0, 1], [1, 1, 19, 0], [17, 2, 17, 3], [1, 0, 2, 1], [11, 2, 11, 3], [19, 2, 18, 3]], 'adelic_image': '20.2.0.?', 'conductor': 4900, 'lmfdb_label': '4900.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 179055
    {'lmfdb_iso': '4900.a', 'p': 11, 'prec': 20, 'unit': 36890420144012623723, 'val': 1}
  • id: 179061
    {'lmfdb_iso': '4900.a', 'p': 13, 'prec': 20, 'unit': 1304238439281266690756, 'val': 1}
  • id: 179063
    {'lmfdb_iso': '4900.a', 'p': 17, 'prec': 20, 'unit': 172697102486666729781852, 'val': 1}
  • id: 179068
    {'lmfdb_iso': '4900.a', 'p': 23, 'prec': 20, 'unit': 18784176012884295247159570, 'val': 1}
  • id: 179060
    {'lmfdb_iso': '4900.a', 'p': 29, 'prec': 20, 'unit': 724649651825211221198172489, 'val': 1}
  • id: 179072
    {'lmfdb_iso': '4900.a', 'p': 31, 'prec': 20, 'unit': 21157246073854684541433974589, 'val': 1}
  • id: 179056
    {'lmfdb_iso': '4900.a', 'p': 37, 'prec': 20, 'unit': 607667703701111962436564143468, 'val': 1}
  • id: 179058
    {'lmfdb_iso': '4900.a', 'p': 41, 'prec': 20, 'unit': 1308868751168827568780959097995, 'val': 1}
  • id: 179059
    {'lmfdb_iso': '4900.a', 'p': 43, 'prec': 20, 'unit': 7138534491245384244001545529655, 'val': 1}
  • id: 179070
    {'lmfdb_iso': '4900.a', 'p': 47, 'prec': 20, 'unit': 35250670708653280311409844473169, 'val': 1}
  • id: 179065
    {'lmfdb_iso': '4900.a', 'p': 53, 'prec': 20, 'unit': 431713050602243652221554795262724, 'val': 1}
  • id: 179066
    {'lmfdb_iso': '4900.a', 'p': 59, 'prec': 20, 'unit': 457457380041013186968942230477899, 'val': 1}
  • id: 179071
    {'lmfdb_iso': '4900.a', 'p': 61, 'prec': 20, 'unit': 3645779705543692916963507767104714, 'val': 1}
  • id: 179064
    {'lmfdb_iso': '4900.a', 'p': 67, 'prec': 20, 'unit': 46817057023087539205342406038240118, 'val': 1}
  • id: 179057
    {'lmfdb_iso': '4900.a', 'p': 71, 'prec': 20, 'unit': 147417757616155229157214783759469517, 'val': 1}
  • id: 179067
    {'lmfdb_iso': '4900.a', 'p': 73, 'prec': 20, 'unit': 158455443793816307177455916587208258, 'val': 1}
  • id: 179062
    {'lmfdb_iso': '4900.a', 'p': 79, 'prec': 20, 'unit': 98423219586122241008392415685959757, 'val': 1}
  • id: 179054
    {'lmfdb_iso': '4900.a', 'p': 83, 'prec': 20, 'unit': 2778578588508321613554770283390215169, 'val': 1}
  • id: 179069
    {'lmfdb_iso': '4900.a', 'p': 89, 'prec': 20, 'unit': 2237704653409928485686425079505392784, 'val': 1}
  • id: 179053
    {'lmfdb_iso': '4900.a', 'p': 97, 'prec': 20, 'unit': 51766082107403794819655792506983571010, 'val': 1}