Elliptic curve data - 57222.m3

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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': '57222s', 'Clabel': '57222s1', 'Cnumber': 1, 'abc_quality': 1.0219861987163863, 'absD': 196227824441026791742636032, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 4488, 'ainvs': [1, -1, 0, -534370302, 4706697104788], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 57222, 'degree': 26542080, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8575515566871823369345964190', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [959024269496848362625, 11151660319506432], 'lmfdb_iso': '57222.m', 'lmfdb_label': '57222.m3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -205448, -35497920], 'min_quad_twist_disc': -51, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '24.24.0.bx.1', '51.8.0-3.a.1.1', '66.24.0.b.1', '102.24.0.?', '264.48.1.?', '408.48.0.?', '1122.48.0.?', '4488.96.1.?'], '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': '3.0182593872605737454548995384', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8916387403250194511122064916', 'prec': 100}, 'szpiro_ratio': 6.56370718320002, '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, -2, -1, 0, 0, 1, 0, -4, 2, 0, 1, 0, 0, 8, 0], 'aplist': [-1, 0, 0, -2, 1, -4, 0, 8, 6, 6, 4, -2, -6, -4, -6, 12, 0, 4, -4, 6, -2, 10, -12, -18, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 57222, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '57222.m', 'trace_hash': 2159805672390127786}
• 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': '0.00044603946943250103083207634433', 'prec': 113}, 'conductor': 57222, 'gens': [[-157, 2188820, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.0182593872605737454548995384', 'prec': 100}], 'lmfdb_label': '57222.m3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.056779171140884523242098975485', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1129823911243849531157582700150626108', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[12236, -6118, 1]], 'xcoord_integral_points': [-157, 12236]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [2, 0], '13': [3, 0], '17': 'a', '19': [1, 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': '57222.m3'}
• ec_torsion_growth •

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

  
  
  • id: 2755980
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 2]}
  • id: 2755981
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '57222.m3', 'torsion': [6]}
  • id: 2755983
    {'degree': 4, 'field': [157, -83, 26, -1, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 6]}
  • id: 2755982
    {'degree': 4, 'field': [569, -10, 45, -2, 1], 'lmfdb_label': '57222.m3', 'torsion': [4]}
  • id: 2755984
    {'degree': 6, 'field': [-17, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '57222.m3', 'torsion': [6]}
  • id: 2755987
    {'degree': 8, 'field': [29241, 0, 8142, 0, 967, 0, 50, 0, 1], 'lmfdb_label': '57222.m3', 'torsion': [12]}
  • id: 2755986
    {'degree': 8, 'field': [36804, 1752, 8746, 772, 671, 46, 53, -2, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 4]}
  • id: 2755985
    {'degree': 8, 'field': [198916, 0, -50471, 0, 195, 0, 127, 0, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 4]}
  • id: 2755988
    {'degree': 12, 'field': [16, -56, 120, -178, 175, 3, -65, 12, 12, -2, 1, -3, 1], 'lmfdb_label': '57222.m3', 'torsion': [3, 6]}
  • id: 2755989
    {'degree': 12, 'field': [23512, 62150, 59213, 36436, 21666, 4012, -335, 170, -315, -46, 2, -2, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 6]}
  • id: 2755992
    {'degree': 16, 'field': [493619377, -191247578, 291774183, -46137846, 46706133, -607548, 4484854, 7936, 433422, -6360, 21630, 2076, 557, 74, 39, -2, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 12]}
  • id: 2755990
    {'degree': 16, 'field': [1092362233, 1089664432, 563990620, 147654064, 26021364, 1530576, -2246940, -1259304, -323495, -2904, -852, 2976, 828, -200, 52, -8, 1], 'lmfdb_label': '57222.m3', 'torsion': [8]}
  • id: 2755991
    {'degree': 16, 'field': [2692779664, 0, 121863432, 0, 89324497, 0, -8806230, 0, 42255, 0, 20580, 0, 367, 0, -54, 0, 1], 'lmfdb_label': '57222.m3', 'torsion': [2, 12]}
  • id: 2755993
    {'degree': 18, 'field': [2652038538201, 3791808633951, 1686812610483, 679767205806, 321350255100, 43157298474, 31126615074, 341564094, 1844540181, -120528657, 73878795, -7374762, 2109388, -144192, 37536, -1120, 321, -3, 1], 'lmfdb_label': '57222.m3', 'torsion': [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: 1375971
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 30, 'j_denominator_valuation': 30, 'kodaira_symbol': 34, 'lmfdb_label': '57222.m3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375972
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '57222.m3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1375973
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '57222.m3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1375974
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57222.m3', 'prime': 17, '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: 2043975
    {'adelic_gens': [[11, 2, 4438, 4479], [1599, 850, 4454, 2381], [3382, 1309, 1683, 2396], [3826, 2907, 3213, 256], [1, 0, 12, 1], [4477, 12, 4476, 13], [1, 6, 6, 37], [1, 12, 0, 1], [3431, 0, 0, 4487], [2245, 2652, 1326, 2449]], 'adelic_image': '4488.96.1.?', 'conductor': 57222, 'lmfdb_label': '57222.m3', 'prime': 0}
  • id: 242831
    {'conductor': 57222, 'elladic_image': '8.6.0.4', 'lmfdb_label': '57222.m3', 'modell_image': '2B', 'prime': 2}
  • id: 242832
    {'conductor': 57222, 'elladic_image': '3.4.0.1', 'lmfdb_label': '57222.m3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2900706
    {'lmfdb_iso': '57222.m', 'p': 7, 'prec': 20, 'unit': 967334605163012, 'val': 1}
  • id: 2900710
    {'lmfdb_iso': '57222.m', 'p': 13, 'prec': 20, 'unit': 14672059834222383069, 'val': 2}
  • id: 2900712
    {'lmfdb_iso': '57222.m', 'p': 19, 'prec': 20, 'unit': 1534205410634140248368006, 'val': 1}
  • id: 2900715
    {'lmfdb_iso': '57222.m', 'p': 23, 'prec': 20, 'unit': 1993991006476123876360165, 'val': 1}
  • id: 2900709
    {'lmfdb_iso': '57222.m', 'p': 29, 'prec': 20, 'unit': 4938386996478371276129777342, 'val': 1}
  • id: 2900720
    {'lmfdb_iso': '57222.m', 'p': 31, 'prec': 20, 'unit': 20158503599421161817757034576, 'val': 1}
  • id: 2900705
    {'lmfdb_iso': '57222.m', 'p': 37, 'prec': 20, 'unit': 39192987551588052287354689981, 'val': 1}
  • id: 2900707
    {'lmfdb_iso': '57222.m', 'p': 41, 'prec': 20, 'unit': 809321194941004726570899033804, 'val': 1}
  • id: 2900708
    {'lmfdb_iso': '57222.m', 'p': 43, 'prec': 20, 'unit': 403802026198048931694022296408, 'val': 1}
  • id: 2900711
    {'lmfdb_iso': '57222.m', 'p': 47, 'prec': 20, 'unit': 21968800334052932741554115242290, 'val': 1}
  • id: 2900713
    {'lmfdb_iso': '57222.m', 'p': 53, 'prec': 20, 'unit': 222994229646221753493265018119682, 'val': 1}
  • id: 2900719
    {'lmfdb_iso': '57222.m', 'p': 61, 'prec': 20, 'unit': 4833092389277888682625618101130221, 'val': 1}
  • id: 2900704
    {'lmfdb_iso': '57222.m', 'p': 67, 'prec': 20, 'unit': 40255673267742189185195487029339713, 'val': 1}
  • id: 2900717
    {'lmfdb_iso': '57222.m', 'p': 71, 'prec': 20, 'unit': 136383573041840494090392377955557471, 'val': 1}
  • id: 2900714
    {'lmfdb_iso': '57222.m', 'p': 73, 'prec': 20, 'unit': 245673845798301609635493976055655563, 'val': 1}
  • id: 2900718
    {'lmfdb_iso': '57222.m', 'p': 79, 'prec': 20, 'unit': 623748784470559222554853541912823026, 'val': 1}
  • id: 2900703
    {'lmfdb_iso': '57222.m', 'p': 83, 'prec': 20, 'unit': 1230772808721581546841919521106986206, 'val': 1}
  • id: 2900716
    {'lmfdb_iso': '57222.m', 'p': 89, 'prec': 20, 'unit': 7660984910434345489025840687586930393, 'val': 1}
  • id: 2900702
    {'lmfdb_iso': '57222.m', 'p': 97, 'prec': 20, 'unit': 1150598641115180418585962001437267735, 'val': 1}