Elliptic curve data - 1859.b1

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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': '1859a', 'Clabel': '1859a3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 53094899, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 7150, 'ainvs': [0, -1, 1, -1321636, -584371175], 'analytic_rank': 1, 'bad_primes': [11, 13], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 1859, 'degree': 10800, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7791837938294154906381091259', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '1859.b', 'lmfdb_label': '1859.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': 13, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '22.2.0.a.1', '25.60.0.a.2', '65.24.0-5.a.2.1', '110.24.1.?', '275.300.12.?', '325.120.0.?', '550.600.37.?', '1430.48.1.?', '3575.600.12.?', '7150.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '32.122151414019583849483096308', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540512', 'prec': 103}, 'szpiro_ratio': 7.15969999186144, '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, 2, 0, -2, -2, -1, -2, 0, 4, 1, -4, -2, -4, 0, -2], 'aplist': [2, -1, -1, 2, -1, 0, -2, 0, -1, 0, -7, -3, 8, -6, -8, -6, -5, 12, 7, 3, -4, -10, 6, -15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 1859, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '1859.b', 'trace_hash': 1458737521272294868}
• 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': '0.028485286514707066426277026336', 'prec': 107}, 'conductor': 1859, 'gens': [[1158131342675917, 39412566954338806189979, 51474]], 'heights': [{'__RealLiteral__': 0, 'data': '32.122151414019583849483096308', 'prec': 100}], 'lmfdb_label': '1859.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.070403065013475481906363918340', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5229958287478482864024234053382733760', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': [1, 0], '5': [1, 2], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1859.b1'}
• ec_torsion_growth •

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

  
  
  • id: 94344
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '1859.b1', 'torsion': [2]}
  • id: 94345
    {'degree': 4, 'field': [61, -16, 16, -1, 1], 'lmfdb_label': '1859.b1', 'torsion': [5]}
  • id: 94346
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '1859.b1', 'torsion': [2, 2]}
  • id: 94347
    {'degree': 8, 'field': [217, 1024, 1015, 327, -33, -24, -2, -2, 1], 'lmfdb_label': '1859.b1', 'torsion': [3]}
  • id: 94348
    {'degree': 10, 'field': [-793, 1300, -965, 1220, -70, -189, 5, 50, -5, -5, 1], 'lmfdb_label': '1859.b1', 'torsion': [5]}
  • id: 94349
    {'degree': 12, 'field': [-236402, -29064, -5324, 33628, 1012, -4556, 1100, 1116, -454, -30, 6, -2, 1], 'lmfdb_label': '1859.b1', 'torsion': [4]}
  • id: 94350
    {'degree': 12, 'field': [112271, 13243, 154932, 9738, 51609, 2304, 9383, 128, 965, -12, 50, -1, 1], 'lmfdb_label': '1859.b1', 'torsion': [10]}
  • id: 94351
    {'degree': 20, 'field': [125449878253501, -40163370590865, 2118659284385, 2775566675165, 136459114540, -39942112252, -14904855615, -11514417090, 4446511965, 1064518715, -280729251, -53983405, 14250070, 1811955, -441670, -43498, 10105, 580, -130, -5, 1], 'lmfdb_label': '1859.b1', 'torsion': [25]}
• 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: 30075
    {'conductor': 1859, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1859.b1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 30076
    {'conductor': 1859, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1859.b1', 'prime': 13, '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: 1676138
    {'adelic_gens': [[2640, 559, 2327, 6813], [38, 41, 4591, 4389], [7101, 50, 7100, 51], [1, 50, 0, 1], [1649, 0, 0, 7149], [1, 0, 50, 1], [2211, 4420, 1365, 6891]], 'adelic_image': '7150.1200.37.?', 'conductor': 1859, 'lmfdb_label': '1859.b1', 'prime': 0}
  • id: 9093
    {'conductor': 1859, 'elladic_image': '25.60.0.2', 'lmfdb_label': '1859.b1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 52979
    {'lmfdb_iso': '1859.b', 'p': 5, 'prec': 20, 'unit': 17655014660612, 'val': 1}
  • id: 52964
    {'lmfdb_iso': '1859.b', 'p': 7, 'prec': 20, 'unit': 11293960559564258, 'val': 1}
  • id: 52969
    {'lmfdb_iso': '1859.b', 'p': 17, 'prec': 20, 'unit': 207346202387899734741225, 'val': 1}
  • id: 52974
    {'lmfdb_iso': '1859.b', 'p': 23, 'prec': 20, 'unit': 63518476355801884349700900, 'val': 1}
  • id: 52965
    {'lmfdb_iso': '1859.b', 'p': 31, 'prec': 20, 'unit': 6009343109305764604275392900, 'val': 1}
  • id: 52963
    {'lmfdb_iso': '1859.b', 'p': 37, 'prec': 20, 'unit': 327479478984771832144863326209, 'val': 1}
  • id: 52966
    {'lmfdb_iso': '1859.b', 'p': 41, 'prec': 20, 'unit': 2176988838578720216370746387084, 'val': 1}
  • id: 52967
    {'lmfdb_iso': '1859.b', 'p': 43, 'prec': 20, 'unit': 4179501194333473666149828585077, 'val': 1}
  • id: 52977
    {'lmfdb_iso': '1859.b', 'p': 47, 'prec': 20, 'unit': 31785508245580916227588565011436, 'val': 1}
  • id: 52971
    {'lmfdb_iso': '1859.b', 'p': 53, 'prec': 20, 'unit': 297879672076499636781465259586667, 'val': 1}
  • id: 52972
    {'lmfdb_iso': '1859.b', 'p': 59, 'prec': 20, 'unit': 22135533177223183759069518143054, 'val': 1}
  • id: 52978
    {'lmfdb_iso': '1859.b', 'p': 61, 'prec': 20, 'unit': 6639190911144766275774599524079672, 'val': 1}
  • id: 52962
    {'lmfdb_iso': '1859.b', 'p': 67, 'prec': 20, 'unit': 44609636315293710884119925753181688, 'val': 1}
  • id: 52976
    {'lmfdb_iso': '1859.b', 'p': 71, 'prec': 20, 'unit': 31298288295821942561213729581357643, 'val': 1}
  • id: 52973
    {'lmfdb_iso': '1859.b', 'p': 73, 'prec': 20, 'unit': 56678303458839209108510654313953645, 'val': 1}
  • id: 52968
    {'lmfdb_iso': '1859.b', 'p': 79, 'prec': 20, 'unit': 343886021676866782084077014495445836, 'val': 1}
  • id: 52970
    {'lmfdb_iso': '1859.b', 'p': 83, 'prec': 20, 'unit': 2263922128129629661421424896074008463, 'val': 1}
  • id: 52975
    {'lmfdb_iso': '1859.b', 'p': 89, 'prec': 20, 'unit': 7393342768951606109151018491662842507, 'val': 1}
  • id: 52961
    {'lmfdb_iso': '1859.b', 'p': 97, 'prec': 20, 'unit': 26717432014088092219956946671479182714, 'val': 1}