Elliptic curve data - 5700.a4

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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': '5700f', 'Clabel': '5700f1', 'Cnumber': 1, 'abc_quality': 1.0493645006386834, 'absD': 328961250000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1140, 'ainvs': [0, -1, 0, -30533, 2063562], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 5700, 'degree': 13824, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2418961701422481218587064492', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [12592337649664, 1315845], 'lmfdb_iso': '5700.a', 'lmfdb_label': '5700.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1221, 16020], 'min_quad_twist_disc': 5, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.1', '10.6.0.a.1', '15.8.0-3.a.1.2', '30.48.0-30.a.1.1', '76.6.0.?', '228.48.0.?', '380.12.0.?', '1140.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7006113559319309770749394601', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 1900], [5, 18, 228], [19, 20, 300]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.20612815373854949808591607544', 'prec': 103}, 'szpiro_ratio': 4.925096569986553, '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, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 0, 0, -6, 0, 1, 0], 'aplist': [0, -1, 0, -2, 0, 4, -6, 1, -6, 6, 8, 4, -6, 10, -6, -12, 12, -10, 4, 0, -14, 8, 18, -6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 5700, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '5700.a', 'trace_hash': 1148336773636630391}
• 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': '0.083426244214750567656300187752', 'prec': 107}, 'conductor': 5700, 'gens': [[98, 54, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7006113559319309770749394601', 'prec': 100}], 'lmfdb_label': '5700.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.92396168184552729780399481559', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1425994571849391831000935101785127332', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[102, 0, 1]], 'xcoord_integral_points': [98, 102]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 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': '5700.a4'}
• ec_torsion_growth •

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

  
  
  • id: 296168
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '5700.a4', 'torsion': [2, 6]}
  • id: 296169
    {'degree': 4, 'field': [1, -2, -16, -2, 1], 'lmfdb_label': '5700.a4', 'torsion': [4]}
  • id: 296170
    {'degree': 6, 'field': [1084, -128, 130, -5, 5, -3, 1], 'lmfdb_label': '5700.a4', 'torsion': [6]}
  • id: 296172
    {'degree': 8, 'field': [-1899, -3402, -1438, 562, 458, 2, -38, -2, 1], 'lmfdb_label': '5700.a4', 'torsion': [2, 12]}
  • id: 296171
    {'degree': 8, 'field': [1681, 0, 3042, 0, 119, 0, 18, 0, 1], 'lmfdb_label': '5700.a4', 'torsion': [2, 12]}
  • id: 296173
    {'degree': 12, 'field': [1175056, -138752, -124536, -5800, 10840, -2622, 1159, 627, -120, -5, 4, -3, 1], 'lmfdb_label': '5700.a4', 'torsion': [6, 6]}
  • id: 296174
    {'degree': 16, 'field': [4071716100, 0, -1115305200, 0, 138602160, 0, -5464440, 0, -1145396, 0, 31176, 0, 2692, 0, -108, 0, 1], 'lmfdb_label': '5700.a4', 'torsion': [8]}
  • id: 296175
    {'degree': 18, 'field': [49722451, 93460611, 25921101, -33493418, 2853972, -4955142, -12389124, -4087410, 913521, 366363, -70287, 27510, 7626, -4164, 324, 188, -51, -3, 1], 'lmfdb_label': '5700.a4', 'torsion': [2, 18]}
• 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: 111907
    {'conductor': 5700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '5700.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 111908
    {'conductor': 5700, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '5700.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 111909
    {'conductor': 5700, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '5700.a4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 111910
    {'conductor': 5700, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5700.a4', 'prime': 19, 'reduction_type': 1, '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: 1701127
    {'adelic_gens': [[389, 2, 438, 13], [1, 0, 12, 1], [99, 478, 686, 1061], [1, 6, 6, 37], [1130, 1137, 939, 8], [11, 2, 1090, 1131], [1, 12, 0, 1], [781, 12, 126, 73], [1129, 12, 1128, 13]], 'adelic_image': '1140.96.1.?', 'conductor': 5700, 'lmfdb_label': '5700.a4', 'prime': 0}
  • id: 28008
    {'conductor': 5700, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5700.a4', 'modell_image': '2B', 'prime': 2}
  • id: 28009
    {'conductor': 5700, 'elladic_image': '3.4.0.1', 'lmfdb_label': '5700.a4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 216795
    {'lmfdb_iso': '5700.a', 'p': 7, 'prec': 20, 'unit': 6515959854155370, 'val': 1}
  • id: 216799
    {'lmfdb_iso': '5700.a', 'p': 13, 'prec': 20, 'unit': 340874991392879595427, 'val': 1}
  • id: 216801
    {'lmfdb_iso': '5700.a', 'p': 17, 'prec': 20, 'unit': 4182393420470074243750, 'val': 1}
  • id: 216806
    {'lmfdb_iso': '5700.a', 'p': 23, 'prec': 20, 'unit': 39802727150898186851966702, 'val': 1}
  • id: 216798
    {'lmfdb_iso': '5700.a', 'p': 29, 'prec': 20, 'unit': 1417089447929776626007840085, 'val': 1}
  • id: 216810
    {'lmfdb_iso': '5700.a', 'p': 31, 'prec': 20, 'unit': 19537669277867052624316629510, 'val': 1}
  • id: 216794
    {'lmfdb_iso': '5700.a', 'p': 37, 'prec': 20, 'unit': 582699826863218449941461995301, 'val': 1}
  • id: 216796
    {'lmfdb_iso': '5700.a', 'p': 41, 'prec': 20, 'unit': 679243001257564136166675874756, 'val': 1}
  • id: 216797
    {'lmfdb_iso': '5700.a', 'p': 43, 'prec': 20, 'unit': 7627624152690927628359414561884, 'val': 1}
  • id: 216808
    {'lmfdb_iso': '5700.a', 'p': 47, 'prec': 20, 'unit': 2711802231259410586115247158821, 'val': 1}
  • id: 216803
    {'lmfdb_iso': '5700.a', 'p': 53, 'prec': 20, 'unit': 459932559284857345548475032343330, 'val': 1}
  • id: 216804
    {'lmfdb_iso': '5700.a', 'p': 59, 'prec': 20, 'unit': 2491844678174190103360313430359416, 'val': 1}
  • id: 216809
    {'lmfdb_iso': '5700.a', 'p': 61, 'prec': 20, 'unit': 1834217140132285826043109813814803, 'val': 1}
  • id: 216793
    {'lmfdb_iso': '5700.a', 'p': 67, 'prec': 20, 'unit': 22770844610376352935735071628607649, 'val': 1}
  • id: 216805
    {'lmfdb_iso': '5700.a', 'p': 73, 'prec': 20, 'unit': 209271683865654174551589165614238894, 'val': 1}
  • id: 216800
    {'lmfdb_iso': '5700.a', 'p': 79, 'prec': 20, 'unit': 1134274908937461216472835948238128821, 'val': 1}
  • id: 216802
    {'lmfdb_iso': '5700.a', 'p': 83, 'prec': 20, 'unit': 2686130276190234638128196584926619263, 'val': 1}
  • id: 216807
    {'lmfdb_iso': '5700.a', 'p': 89, 'prec': 20, 'unit': 240448359108451004610729411835384761, 'val': 1}
  • id: 216792
    {'lmfdb_iso': '5700.a', 'p': 97, 'prec': 20, 'unit': 39545956705975576923952591251094554678, 'val': 1}