Elliptic curve data - 196.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
  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': '196a', 'Clabel': '196a2', 'Cnumber': 2, 'abc_quality': 0.9989714715999977, 'absD': 784, 'adelic_genus': 28, 'adelic_index': 864, 'adelic_level': 252, 'ainvs': [0, -1, 0, -142, 701], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 196, 'degree': 18, 'elladic_images': ['2.2.0.1', '9.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.20503477820738141011106300958', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [406749952, 1], 'lmfdb_iso': '196.a', 'lmfdb_label': '196.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -142, 701], 'min_quad_twist_disc': 1, 'modell_images': ['2Cn', '3B'], 'modm_images': ['2.2.0.a.1', '3.4.0.a.1', '6.8.0.a.1', '9.12.0.b.1', '12.16.0.a.1', '14.6.0.a.1', '18.72.2.c.1', '21.8.0-3.a.1.2', '28.12.0-14.a.1.1', '36.144.6.i.2', '42.48.0-42.a.1.2', '63.72.0-63.h.1.3', '84.96.2.?', '126.432.10.?', '252.864.28.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.25810635289973679058716498246', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [7, 14, 4]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76040219656991539743436584064', 'prec': 107}, 'szpiro_ratio': 5.018481013875294, '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, -1, 0, -3, 0, 0, 0, -2, 0, -3, 0, -2, 0, 3, 0, -3, 0, 1, 0], 'aplist': [0, -1, -3, 0, -3, -2, -3, 1, 3, -6, 7, -1, -6, -4, 9, 3, -9, 1, -7, 0, 1, -13, -12, -15, 10], 'class_deg': 3, 'class_size': 2, 'conductor': 196, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '196.a', 'trace_hash': 1449284123912416083}
• 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': '1.5069225976008350668148024175', 'prec': 100}, 'conductor': 196, 'gens': [[7, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25810635289973679058716498246', 'prec': 103}], 'lmfdb_label': '196.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.3609185288243093391936038281', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1255807767677281735952769161097942985', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [-1, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '196.a1'}
• ec_torsion_growth •

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

  
  
  • id: 7928
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '196.a1', 'torsion': [3]}
  • id: 7929
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '196.a1', 'torsion': [2, 2]}
  • id: 7931
    {'degree': 6, 'field': [1, -8, 8, 6, -6, -1, 1], 'lmfdb_label': '196.a1', 'torsion': [2, 6]}
  • id: 7930
    {'degree': 6, 'field': [1, -4, 9, 6, -3, -2, 1], 'lmfdb_label': '196.a1', 'torsion': [3]}
  • id: 7933
    {'degree': 12, 'field': [1, -5, 21, -22, 19, 21, -20, 21, 3, -8, 7, -3, 1], 'lmfdb_label': '196.a1', 'torsion': [3, 3]}
  • id: 7932
    {'degree': 12, 'field': [1, 2, -20, 38, -46, 74, -120, 124, -71, 18, 4, -4, 1], 'lmfdb_label': '196.a1', 'torsion': [2, 4]}
  • id: 7934
    {'degree': 18, 'field': [-125, 225, -1350, 1941, 4455, -1809, -4411, -426, 2511, 1327, -828, -648, 112, 159, 36, -20, -15, 0, 1], 'lmfdb_label': '196.a1', 'torsion': [9]}
  • id: 7935
    {'degree': 18, 'field': [1, -10, 58, -171, 378, -673, 1016, -1316, 1488, -1479, 1301, -1007, 684, -403, 204, -86, 29, -7, 1], 'lmfdb_label': '196.a1', 'torsion': [2, 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: 1593
    {'conductor': 196, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '196.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1594
    {'conductor': 196, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '196.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

  
  
  • id: 1666574
    {'adelic_gens': [[146, 9, 45, 131], [163, 36, 114, 47], [217, 36, 216, 37], [1, 0, 36, 1], [127, 36, 18, 145], [31, 6, 112, 103], [1, 36, 0, 1], [19, 36, 42, 199]], 'adelic_image': '252.864.28.?', 'conductor': 196, 'lmfdb_label': '196.a1', 'prime': 0}
  • id: 780
    {'conductor': 196, 'elladic_image': '2.2.0.1', 'lmfdb_label': '196.a1', 'modell_image': '2Cn', 'prime': 2}
  • id: 781
    {'conductor': 196, 'elladic_image': '9.12.0.2', 'lmfdb_label': '196.a1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1436
    {'lmfdb_iso': '196.a', 'p': 5, 'prec': 20, 'unit': 11128877070222, 'val': 1}
  • id: 1435
    {'lmfdb_iso': '196.a', 'p': 11, 'prec': 20, 'unit': 20573140323692048186, 'val': 1}
  • id: 1441
    {'lmfdb_iso': '196.a', 'p': 13, 'prec': 20, 'unit': 1443296258862530675420, 'val': 1}
  • id: 1443
    {'lmfdb_iso': '196.a', 'p': 17, 'prec': 20, 'unit': 139522332863068157134387, 'val': 1}
  • id: 1444
    {'lmfdb_iso': '196.a', 'p': 19, 'prec': 20, 'unit': 585728718938485493444694, 'val': -1}
  • id: 1448
    {'lmfdb_iso': '196.a', 'p': 23, 'prec': 20, 'unit': 20985592583290705233942882, 'val': 1}
  • id: 1440
    {'lmfdb_iso': '196.a', 'p': 29, 'prec': 20, 'unit': 34572148045670397987068197, 'val': 2}
  • id: 1437
    {'lmfdb_iso': '196.a', 'p': 31, 'prec': 20, 'unit': 5993273169330566144992953, 'val': 2}
  • id: 1453
    {'lmfdb_iso': '196.a', 'p': 37, 'prec': 20, 'unit': 524002326228991768412239813129, 'val': 1}
  • id: 1438
    {'lmfdb_iso': '196.a', 'p': 41, 'prec': 20, 'unit': 3568246082124471735371969573191, 'val': 1}
  • id: 1439
    {'lmfdb_iso': '196.a', 'p': 43, 'prec': 20, 'unit': 7543671664560636023506897320705, 'val': 1}
  • id: 1450
    {'lmfdb_iso': '196.a', 'p': 47, 'prec': 20, 'unit': 50940938092901109821204116843814, 'val': 1}
  • id: 1445
    {'lmfdb_iso': '196.a', 'p': 53, 'prec': 20, 'unit': 156279356743297465864128628644736, 'val': 1}
  • id: 1446
    {'lmfdb_iso': '196.a', 'p': 59, 'prec': 20, 'unit': 3484518069741267830401747668862857, 'val': 1}
  • id: 1451
    {'lmfdb_iso': '196.a', 'p': 61, 'prec': 20, 'unit': 253737088173799900355444424702945720, 'val': -1}
  • id: 1434
    {'lmfdb_iso': '196.a', 'p': 67, 'prec': 20, 'unit': 11842538483689690380403370304222882, 'val': 1}
  • id: 1447
    {'lmfdb_iso': '196.a', 'p': 73, 'prec': 20, 'unit': 18452075754862480082368352782641305030, 'val': 0}
  • id: 1442
    {'lmfdb_iso': '196.a', 'p': 79, 'prec': 20, 'unit': 522265302923699508580751553545777111, 'val': 1}
  • id: 1452
    {'lmfdb_iso': '196.a', 'p': 83, 'prec': 20, 'unit': 615127789508558101896037485208940290, 'val': 1}
  • id: 1449
    {'lmfdb_iso': '196.a', 'p': 89, 'prec': 20, 'unit': 2477494523880966271312834538948743441, 'val': 1}
  • id: 1433
    {'lmfdb_iso': '196.a', 'p': 97, 'prec': 20, 'unit': 9553114995508856265526210166397149635, 'val': 1}