Elliptic curve data - 5610.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
  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': '5610d', 'Clabel': '5610d1', 'Cnumber': 1, 'abc_quality': 0.834779256033568, 'absD': 2098140, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2040, 'ainvs': [1, 1, 0, 27, 57], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5610, 'degree': 1024, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10011667398738112381158341046', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [2053225511, 2098140], 'lmfdb_iso': '5610.b', 'lmfdb_label': '5610.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 27, 57], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '30.6.0.a.1', '136.6.0.?', '2040.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.60371828463256927554288124866', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 4, 15], [3, 4, 1870], [5, 6, 1122], [11, 12, 510], [17, 18, 330]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10011667398738112381158341046', 'prec': 107}, 'szpiro_ratio': 2.4840034420991075, '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, -2, -1, 1, 1, 1, -1, 0, 2, 1, 1, 1, -1, 0, -1], 'aplist': [-1, -1, -1, -2, 1, 0, 1, 0, -4, 2, 4, -2, 0, -6, 0, -6, 14, -2, 14, -2, 16, 12, 0, -18, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 5610, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5610.b', 'trace_hash': 2028585522191883124}
• 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': '1.2216878032762123825137818446', 'prec': 100}, 'conductor': 5610, 'gens': [[-1, 6, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.60371828463256927554288124866', 'prec': 103}], 'lmfdb_label': '5610.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7234057939580302459097554255', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0809031793083462852623416535884711199', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-2, 1, 1]], 'xcoord_integral_points': [-2, -1, 7, 32]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [1, 0], '5': [3, 0], '7': [1, 0], '11': [4, 0], '13': [1, 1, 0], '17': [2, 0], '19': [1, 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]}, 'iwp0': 0, 'lmfdb_label': '5610.b2'}
• ec_torsion_growth •

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

  
  
  • id: 291795
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '5610.b2', 'torsion': [2, 2]}
  • id: 291796
    {'degree': 4, 'field': [-135, 0, 2, 0, 1], 'lmfdb_label': '5610.b2', 'torsion': [4]}
  • id: 291799
    {'degree': 8, 'field': [-17662, -5195, 5672, -955, 481, -7, 7, -4, 1], 'lmfdb_label': '5610.b2', 'torsion': [6]}
  • id: 291798
    {'degree': 8, 'field': [519, -282, 1237, -758, 674, -110, 17, -2, 1], 'lmfdb_label': '5610.b2', 'torsion': [2, 4]}
  • id: 291797
    {'degree': 8, 'field': [1156, -4444, 4769, -1498, 1144, -116, -4, -2, 1], 'lmfdb_label': '5610.b2', 'torsion': [2, 4]}
  • id: 291800
    {'degree': 16, 'field': [57121, 0, -274803088, 0, -38132808, 0, 10485112, 0, 750382, 0, -9872, 0, -1128, 0, 8, 0, 1], 'lmfdb_label': '5610.b2', 'torsion': [8]}
  • id: 291801
    {'degree': 16, 'field': [12027024, 0, -14104356, 0, 17906440, 0, 1088952, 0, 35085, 0, 6452, 0, 402, 0, 0, 0, 1], 'lmfdb_label': '5610.b2', '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: 109903
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5610.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 109904
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 109905
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 109906
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5610.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 109907
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5610.b2', 'prime': 17, '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: 1700533
    {'adelic_gens': [[1, 2, 2, 5], [257, 1786, 1784, 255], [1, 4, 0, 1], [1021, 4, 2, 9], [241, 4, 482, 9], [682, 1, 679, 0], [1, 0, 4, 1], [2037, 4, 2036, 5], [3, 4, 8, 11], [1634, 1, 1223, 0]], 'adelic_image': '2040.12.0.?', 'conductor': 5610, 'lmfdb_label': '5610.b2', 'prime': 0}
  • id: 27595
    {'conductor': 5610, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5610.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 212159
    {'lmfdb_iso': '5610.b', 'p': 7, 'prec': 20, 'unit': 2279261966915677, 'val': 1}
  • id: 212165
    {'lmfdb_iso': '5610.b', 'p': 23, 'prec': 20, 'unit': 64734128336473085216315198, 'val': 1}
  • id: 212162
    {'lmfdb_iso': '5610.b', 'p': 29, 'prec': 20, 'unit': 1280135289014089296396357017, 'val': 1}
  • id: 212170
    {'lmfdb_iso': '5610.b', 'p': 31, 'prec': 20, 'unit': 21611408017171768526274506110, 'val': 1}
  • id: 212158
    {'lmfdb_iso': '5610.b', 'p': 37, 'prec': 20, 'unit': 142721006200503711374731485658, 'val': 1}
  • id: 212161
    {'lmfdb_iso': '5610.b', 'p': 43, 'prec': 20, 'unit': 4222445762273811108594585648090, 'val': 1}
  • id: 212164
    {'lmfdb_iso': '5610.b', 'p': 53, 'prec': 20, 'unit': 388414413533198796988142222607624, 'val': 1}
  • id: 212168
    {'lmfdb_iso': '5610.b', 'p': 59, 'prec': 20, 'unit': 336194876178862633195611823546187, 'val': 1}
  • id: 212169
    {'lmfdb_iso': '5610.b', 'p': 61, 'prec': 20, 'unit': 7192966061466470938335427806188956, 'val': 1}
  • id: 212157
    {'lmfdb_iso': '5610.b', 'p': 67, 'prec': 20, 'unit': 71330088128851933505224895985767, 'val': 1}
  • id: 212167
    {'lmfdb_iso': '5610.b', 'p': 71, 'prec': 20, 'unit': 120725125391977071677544873291897068, 'val': 1}
  • id: 212160
    {'lmfdb_iso': '5610.b', 'p': 73, 'prec': 20, 'unit': 189142979636316351808047920349277960, 'val': 1}
  • id: 212163
    {'lmfdb_iso': '5610.b', 'p': 79, 'prec': 20, 'unit': 914743308924496849347466765040682473, 'val': 1}
  • id: 212166
    {'lmfdb_iso': '5610.b', 'p': 89, 'prec': 20, 'unit': 8604961579221040041268716475848041084, 'val': 1}