Elliptic curve data - 18735.b2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '18735b', 'Clabel': '18735b1', 'Cnumber': 1, 'abc_quality': 0.7632428472333861, 'absD': 281025, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 74940, 'ainvs': [1, 0, 0, -31, -64], 'analytic_rank': 1, 'bad_primes': [3, 5, 1249], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 18735, 'degree': 2816, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.21311966694598403247621748082', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [3301293169, 281025], 'lmfdb_iso': '18735.b', 'lmfdb_label': '18735.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -31, -64], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.b.1', '2498.6.0.?', '74940.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1528198061358049011182391136', 'prec': 100}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.21311966694598403247621748082', 'prec': 107}, 'szpiro_ratio': 2.227815490635813, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [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, -1, -1, 4, 3, 1, 1, 4, -1, -2, -4, -1, -1, -6, -1, 2, 1], 'aplist': [-1, 1, -1, 4, 4, -2, -6, 2, 6, -8, 4, -6, 0, 8, 0, -10, 0, -10, -12, -4, -14, 8, 4, -4, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 18735, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '18735.b', 'trace_hash': 1978955192673648138}
• 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': '1.5314872680827757627142083472', 'prec': 100}, 'conductor': 18735, 'gens': [[16, 52, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1528198061358049011182391136', 'prec': 100}], 'lmfdb_label': '18735.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.0339235080878289788595240171', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3786708123766961941274682223287992458', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-4, 2, 1]], 'xcoord_integral_points': [-4, 16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0], '1249': 'o?'}, 'iwp0': 0, 'lmfdb_label': '18735.b2'}
• ec_torsion_growth •

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

  
  
  • id: 959178
    {'degree': 2, 'field': [-312, -1, 1], 'lmfdb_label': '18735.b2', 'torsion': [2, 2]}
  • id: 959179
    {'degree': 4, 'field': [84, -24, 25, -2, 1], 'lmfdb_label': '18735.b2', 'torsion': [4]}
  • id: 959182
    {'degree': 8, 'field': [-27675, 6912, -7470, 1115, -554, -7, 7, -4, 1], 'lmfdb_label': '18735.b2', 'torsion': [6]}
  • id: 959181
    {'degree': 8, 'field': [57600, 0, -257372, 0, -7303, 0, -94, 0, 1], 'lmfdb_label': '18735.b2', 'torsion': [2, 4]}
  • id: 959180
    {'degree': 8, 'field': [1368900, 0, -35160, 0, 2629, 0, 34, 0, 1], 'lmfdb_label': '18735.b2', 'torsion': [2, 4]}
  • id: 959184
    {'degree': 16, 'field': [455625, 0, -40576275, 0, -65141325, 0, -47676330, 0, -9619293, 0, -468214, 0, -7674, 0, 0, 0, 1], 'lmfdb_label': '18735.b2', 'torsion': [2, 6]}
  • id: 959183
    {'degree': 16, 'field': [111667761, -262663344, 357293556, -203019336, 136865658, -45156744, 19739544, -4301808, 1449043, -278504, 86536, -18608, 4618, -728, 124, -8, 1], 'lmfdb_label': '18735.b2', 'torsion': [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: 422337
    {'conductor': 18735, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '18735.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 422338
    {'conductor': 18735, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '18735.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 422339
    {'conductor': 18735, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '18735.b2', 'prime': 1249, 'reduction_type': 1, '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: 1789187
    {'adelic_gens': [[1, 0, 4, 1], [29977, 4, 59954, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [74937, 4, 74936, 5], [49961, 4, 24982, 9], [15002, 1, 67439, 0], [56209, 18736, 56204, 18735]], 'adelic_image': '74940.12.0.?', 'conductor': 18735, 'lmfdb_label': '18735.b2', 'prime': 0}
  • id: 87655
    {'conductor': 18735, 'elladic_image': '2.3.0.1', 'lmfdb_label': '18735.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 863999
    {'lmfdb_iso': '18735.b', 'p': 7, 'prec': 20, 'unit': 4626778846430793, 'val': 1}
  • id: 864005
    {'lmfdb_iso': '18735.b', 'p': 11, 'prec': 20, 'unit': 36691610500001754565, 'val': 1}
  • id: 864003
    {'lmfdb_iso': '18735.b', 'p': 13, 'prec': 20, 'unit': 1063122631832257178167, 'val': 1}
  • id: 864006
    {'lmfdb_iso': '18735.b', 'p': 17, 'prec': 20, 'unit': 9300311120190916143254, 'val': 1}
  • id: 864007
    {'lmfdb_iso': '18735.b', 'p': 19, 'prec': 20, 'unit': 1664675315485280200014339, 'val': 1}
  • id: 864009
    {'lmfdb_iso': '18735.b', 'p': 23, 'prec': 20, 'unit': 24770905682640858122479531, 'val': 1}
  • id: 864002
    {'lmfdb_iso': '18735.b', 'p': 29, 'prec': 20, 'unit': 2171228476262931440622537335, 'val': 1}
  • id: 864013
    {'lmfdb_iso': '18735.b', 'p': 31, 'prec': 20, 'unit': 13944447400425337444809560997, 'val': 1}
  • id: 863998
    {'lmfdb_iso': '18735.b', 'p': 37, 'prec': 20, 'unit': 426705938480334604503182418355, 'val': 1}
  • id: 864001
    {'lmfdb_iso': '18735.b', 'p': 43, 'prec': 20, 'unit': 7490132146958027861644136657272, 'val': 1}
  • id: 864008
    {'lmfdb_iso': '18735.b', 'p': 53, 'prec': 20, 'unit': 395686545774780197053820278038391, 'val': 1}
  • id: 864012
    {'lmfdb_iso': '18735.b', 'p': 61, 'prec': 20, 'unit': 4858258217454413119900081267224291, 'val': 1}
  • id: 863997
    {'lmfdb_iso': '18735.b', 'p': 67, 'prec': 20, 'unit': 43250966595978672420979194325574786, 'val': 1}
  • id: 864011
    {'lmfdb_iso': '18735.b', 'p': 71, 'prec': 20, 'unit': 128573320662741632493978926409532848, 'val': 1}
  • id: 864000
    {'lmfdb_iso': '18735.b', 'p': 73, 'prec': 20, 'unit': 12843888046060690126594296917797757, 'val': 1}
  • id: 864004
    {'lmfdb_iso': '18735.b', 'p': 79, 'prec': 20, 'unit': 880489630238676914936850315940605403, 'val': 1}
  • id: 863996
    {'lmfdb_iso': '18735.b', 'p': 83, 'prec': 20, 'unit': 621133830995997470867874315823480572, 'val': 1}
  • id: 864010
    {'lmfdb_iso': '18735.b', 'p': 89, 'prec': 20, 'unit': 9589586998386637483662673375960638053, 'val': 1}
  • id: 863995
    {'lmfdb_iso': '18735.b', 'p': 97, 'prec': 20, 'unit': 955803942564041115355702444559873436, 'val': 1}