Elliptic curve data - 22050.ba2

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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': '22050bi', 'Clabel': '22050bi5', 'Cnumber': 5, 'abc_quality': 1.0293250379726038, 'absD': 2459086221312000000, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 2520, 'ainvs': [1, -1, 0, -1879992, -994555584], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 22050, 'degree': 497664, 'elladic_images': ['8.6.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3935075652218734884228449509', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 9, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [-548347731625, 1835008], 'lmfdb_iso': '22050.ba', 'lmfdb_label': '22050.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -171, -874], 'min_quad_twist_disc': 105, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '9.12.0.a.1', '14.6.0.b.1', '18.36.0.a.1', '24.24.0.bw.1', '30.24.0-6.a.1.3', '42.24.0.b.1', '56.12.0.n.1', '63.36.0.d.1', '72.72.1.?', '90.72.0.?', '105.8.0.?', '120.48.0.?', '126.216.7.?', '168.48.1.?', '210.48.0.?', '315.72.0.?', '360.144.1.?', '504.432.21.?', '630.432.7.?', '840.96.1.?', '2520.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5314926812654806460044713198', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 11025], [3, 6, 1225], [5, 14, 882], [7, 32, 450]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.066527390143111802872166294101', 'prec': 107}, 'szpiro_ratio': 5.495383513340652, '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, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 1, -6, 0, -2, 0], 'aplist': [-1, 0, 0, 0, 0, -4, -6, -2, 0, 6, 4, -2, 6, -8, 12, 6, -6, -8, 4, 0, 2, 8, 6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 22050, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '22050.ba', 'trace_hash': 12133487360906702}
• 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': '0.0083373060494667180523741427583', 'prec': 110}, 'conductor': 22050, 'gens': [[35911, 6684439, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5314926812654806460044713198', 'prec': 100}], 'lmfdb_label': '22050.ba2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.064453058648722025667267803288', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3677974467944216023702447930267287806', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[1584, -792, 1]], 'xcoord_integral_points': [1584]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': 'a', '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '22050.ba2'}
• ec_torsion_growth •

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

  
  
  • id: 1119069
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 2]}
  • id: 1119070
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '22050.ba2', 'torsion': [6]}
  • id: 1119071
    {'degree': 4, 'field': [-89, -22, -7, -2, 1], 'lmfdb_label': '22050.ba2', 'torsion': [4]}
  • id: 1119072
    {'degree': 4, 'field': [4, 2, 5, -1, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 6]}
  • id: 1119073
    {'degree': 6, 'field': [-56, 0, 0, -91, 0, 0, 1], 'lmfdb_label': '22050.ba2', 'torsion': [6]}
  • id: 1119074
    {'degree': 6, 'field': [2961, -2898, 756, -98, 42, 0, 1], 'lmfdb_label': '22050.ba2', 'torsion': [18]}
  • id: 1119077
    {'degree': 8, 'field': [639, -1386, 1167, -678, 304, -74, 33, -2, 1], 'lmfdb_label': '22050.ba2', 'torsion': [12]}
  • id: 1119075
    {'degree': 8, 'field': [1449, 882, -87, -150, -2, 26, -1, -2, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 4]}
  • id: 1119076
    {'degree': 8, 'field': [13714, 3838, 3137, 334, 189, 30, 15, -2, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 4]}
  • id: 1119078
    {'degree': 12, 'field': [1884, -5184, 5529, -2910, 1752, -2058, 1471, -504, 123, -58, 24, -6, 1], 'lmfdb_label': '22050.ba2', 'torsion': [3, 6]}
  • id: 1119080
    {'degree': 12, 'field': [4096, -8706, 11769, -7420, 7185, -4866, 2855, -1206, 495, -140, 39, -6, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 6]}
  • id: 1119079
    {'degree': 12, 'field': [12096, 0, 0, -4032, 0, 0, 823, 0, 0, -52, 0, 0, 1], 'lmfdb_label': '22050.ba2', 'torsion': [18]}
  • id: 1119081
    {'degree': 12, 'field': [92709, -186894, 145665, -76506, 38358, -13350, 3961, -1182, 222, -18, 9, -6, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 18]}
  • id: 1119083
    {'degree': 16, 'field': [639, -1872, 6342, -3804, 7858, -4496, 4330, -1176, -1125, 824, -126, -8, 12, 0, 4, -4, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 12]}
  • id: 1119084
    {'degree': 16, 'field': [26119, -45472, 17298, 1956, 14590, -15776, 8514, -7368, 5511, -1704, 618, -248, 64, 0, 0, -4, 1], 'lmfdb_label': '22050.ba2', 'torsion': [2, 12]}
  • id: 1119082
    {'degree': 16, 'field': [6321169, 18850668, 6842306, 19878480, 539251, 3619160, -821050, -511932, 149910, -4340, -17398, 3128, -571, 56, 2, -4, 1], 'lmfdb_label': '22050.ba2', '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: 502634
    {'conductor': 22050, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '22050.ba2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 502635
    {'conductor': 22050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '22050.ba2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 502636
    {'conductor': 22050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '22050.ba2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 502637
    {'conductor': 22050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '22050.ba2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1811244
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [1261, 540, 10, 361], [19, 36, 720, 1099], [2485, 36, 2484, 37], [1619, 1980, 920, 979], [1724, 495, 785, 1334], [503, 0, 0, 2519], [631, 540, 1270, 361], [1, 18, 14, 253]], 'adelic_image': '2520.864.21.?', 'conductor': 22050, 'lmfdb_label': '22050.ba2', 'prime': 0}
  • id: 101766
    {'conductor': 22050, 'elladic_image': '8.6.0.1', 'lmfdb_label': '22050.ba2', 'modell_image': '2B', 'prime': 2}
  • id: 101767
    {'conductor': 22050, 'elladic_image': '9.12.0.1', 'lmfdb_label': '22050.ba2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1036189
    {'lmfdb_iso': '22050.ba', 'p': 13, 'prec': 20, 'unit': 1458032688627662608993, 'val': 1}
  • id: 1036191
    {'lmfdb_iso': '22050.ba', 'p': 17, 'prec': 20, 'unit': 34850626169209179862958, 'val': 1}
  • id: 1036192
    {'lmfdb_iso': '22050.ba', 'p': 19, 'prec': 20, 'unit': 234792218043298530505937, 'val': 1}
  • id: 1036188
    {'lmfdb_iso': '22050.ba', 'p': 29, 'prec': 20, 'unit': 1715466965255583638090677318, 'val': 1}
  • id: 1036199
    {'lmfdb_iso': '22050.ba', 'p': 31, 'prec': 20, 'unit': 262394846813457420985183130, 'val': 2}
  • id: 1036185
    {'lmfdb_iso': '22050.ba', 'p': 37, 'prec': 20, 'unit': 177962476541244306463468052803, 'val': 1}
  • id: 1036186
    {'lmfdb_iso': '22050.ba', 'p': 41, 'prec': 20, 'unit': 83448987240186806195068300099, 'val': 1}
  • id: 1036187
    {'lmfdb_iso': '22050.ba', 'p': 43, 'prec': 20, 'unit': 3448782198288100485976980285745, 'val': 1}
  • id: 1036197
    {'lmfdb_iso': '22050.ba', 'p': 47, 'prec': 20, 'unit': 20612232955505462023144369588995, 'val': 1}
  • id: 1036193
    {'lmfdb_iso': '22050.ba', 'p': 53, 'prec': 20, 'unit': 51241228375079939751511173798911, 'val': 1}
  • id: 1036194
    {'lmfdb_iso': '22050.ba', 'p': 59, 'prec': 20, 'unit': 3966967371534066689319439583555840, 'val': 1}
  • id: 1036198
    {'lmfdb_iso': '22050.ba', 'p': 61, 'prec': 20, 'unit': 4159569927942364582133459289939348, 'val': 1}
  • id: 1036184
    {'lmfdb_iso': '22050.ba', 'p': 67, 'prec': 20, 'unit': 430733836296595458964730175114890, 'val': 1}
  • id: 1036195
    {'lmfdb_iso': '22050.ba', 'p': 73, 'prec': 20, 'unit': 1841599505968212982853502309043935, 'val': 2}
  • id: 1036190
    {'lmfdb_iso': '22050.ba', 'p': 79, 'prec': 20, 'unit': 123473725829298097820926490562737439, 'val': 1}
  • id: 1036183
    {'lmfdb_iso': '22050.ba', 'p': 83, 'prec': 20, 'unit': 922948241705716710518989331187091408, 'val': 1}
  • id: 1036196
    {'lmfdb_iso': '22050.ba', 'p': 89, 'prec': 20, 'unit': 10258915585136530417867461100482753084, 'val': 1}
  • id: 1036182
    {'lmfdb_iso': '22050.ba', 'p': 97, 'prec': 20, 'unit': 12320698483851935658691639392659911193, 'val': 1}