Elliptic curve data - 57222.z2

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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': '57222t', 'Clabel': '57222t1', 'Cnumber': 1, 'abc_quality': 1.028917697425881, 'absD': 5985050002798652389261836288, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [1, -1, 0, -1071058041, 12968401028589], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 57222, 'degree': 37380096, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0930002415643617193153834341', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [7722211175253055152433, 340131399900069888], 'lmfdb_iso': '57222.z', 'lmfdb_label': '57222.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -411787, -97932871], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '66.6.0.a.1', '136.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '37.509945760422222536046368321', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 28611], [3, 8, 6358], [11, 12, 5202], [13, 2, 28611], [17, 162, 198]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1270874252021988334929935067', 'prec': 100}, 'szpiro_ratio': 6.754122332684399, '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, 2, 0, 2, -1, 0, -2, 1, 0, 4, -2, 0, 1, 0, 0, -2, 2], 'aplist': [-1, 0, 2, 2, 1, 4, 0, -2, 2, 6, -8, -2, -2, -2, -4, -12, 10, -6, -12, 6, -8, 2, 4, 2, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 57222, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '57222.z', 'trace_hash': 679615865627175411}
• 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': '0.00027852562748694155191746120777', 'prec': 113}, 'conductor': 57222, 'gens': [[685798721814952825, 722298539087366089563876316, 7801703]], 'heights': [{'__RealLiteral__': 0, 'data': '37.509945760422222536046368321', 'prec': 100}], 'lmfdb_label': '57222.z2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.042101513211293975370412818313', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3169019079493465729536917853823210288', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[21858, -10929, 1]], 'xcoord_integral_points': [21858]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 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.z2'}
• ec_torsion_growth •

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

  
  
  • id: 2756036
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '57222.z2', 'torsion': [2, 2]}
  • id: 2756037
    {'degree': 4, 'field': [47, 18, -17, -2, 1], 'lmfdb_label': '57222.z2', 'torsion': [4]}
  • id: 2756040
    {'degree': 8, 'field': [-266168, 9725, -7946, -3559, 1783, -7, 7, -4, 1], 'lmfdb_label': '57222.z2', 'torsion': [6]}
  • id: 2756039
    {'degree': 8, 'field': [1089, 0, -2178, 0, 1159, 0, -70, 0, 1], 'lmfdb_label': '57222.z2', 'torsion': [2, 4]}
  • id: 2756038
    {'degree': 8, 'field': [9552, -12288, 5532, -696, -386, 100, 39, -2, 1], 'lmfdb_label': '57222.z2', 'torsion': [2, 4]}
  • id: 2756042
    {'degree': 16, 'field': [477935298, 8120885841, -10018274724, 6772962873, -3414914211, 1457198775, -442817045, 82452326, -10722735, 1145215, 90506, -70227, 8135, 49, -9, -4, 1], 'lmfdb_label': '57222.z2', 'torsion': [2, 6]}
  • id: 2756041
    {'degree': 16, 'field': [32806476868, -32629384656, -24392580696, -14066819184, -773150818, 1340031528, 69460776, -18409776, 5712891, -1463496, -457368, 47736, 14306, -408, -204, 0, 1], 'lmfdb_label': '57222.z2', '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: 1375987
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 26, 'j_denominator_valuation': 26, 'kodaira_symbol': 30, 'lmfdb_label': '57222.z2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1375988
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 19, 'j_denominator_valuation': 13, 'kodaira_symbol': -17, 'lmfdb_label': '57222.z2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1375989
    {'conductor': 57222, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57222.z2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1375990
    {'conductor': 57222, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57222.z2', '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: 2044001
    {'adelic_gens': [[1498, 1, 1495, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1057, 4, 2114, 9], [2245, 4, 2, 9], [3929, 562, 560, 3927], [818, 1, 4079, 0], [4485, 4, 4484, 5]], 'adelic_image': '4488.12.0.?', 'conductor': 57222, 'lmfdb_label': '57222.z2', 'prime': 0}
  • id: 242854
    {'conductor': 57222, 'elladic_image': '2.3.0.1', 'lmfdb_label': '57222.z2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2900724
    {'lmfdb_iso': '57222.z', 'p': 5, 'prec': 20, 'unit': 3539595880782, 'val': 1}
  • id: 2900725
    {'lmfdb_iso': '57222.z', 'p': 7, 'prec': 20, 'unit': 3292249196126847, 'val': 1}
  • id: 2900730
    {'lmfdb_iso': '57222.z', 'p': 13, 'prec': 20, 'unit': 643744890756084346771, 'val': 1}
  • id: 2900733
    {'lmfdb_iso': '57222.z', 'p': 19, 'prec': 20, 'unit': 1845532997120773301891232, 'val': 1}
  • id: 2900736
    {'lmfdb_iso': '57222.z', 'p': 23, 'prec': 20, 'unit': 60697424637930006526748169, 'val': 1}
  • id: 2900729
    {'lmfdb_iso': '57222.z', 'p': 29, 'prec': 20, 'unit': 5642365534517027718235601373, 'val': 1}
  • id: 2900726
    {'lmfdb_iso': '57222.z', 'p': 31, 'prec': 20, 'unit': 15358012613808008783672701341, 'val': 1}
  • id: 2900741
    {'lmfdb_iso': '57222.z', 'p': 37, 'prec': 20, 'unit': 452911864540291786139669992101, 'val': 1}
  • id: 2900727
    {'lmfdb_iso': '57222.z', 'p': 41, 'prec': 20, 'unit': 1978032968074763279598457147881, 'val': 1}
  • id: 2900728
    {'lmfdb_iso': '57222.z', 'p': 43, 'prec': 20, 'unit': 2725864800187427805633037698843, 'val': 1}
  • id: 2900739
    {'lmfdb_iso': '57222.z', 'p': 47, 'prec': 20, 'unit': 36710051906623635629386067441005, 'val': 1}
  • id: 2900734
    {'lmfdb_iso': '57222.z', 'p': 53, 'prec': 20, 'unit': 434742716832410130250901671899415, 'val': 1}
  • id: 2900732
    {'lmfdb_iso': '57222.z', 'p': 59, 'prec': 20, 'unit': 1621942199679213318858936250245952, 'val': 1}
  • id: 2900740
    {'lmfdb_iso': '57222.z', 'p': 61, 'prec': 20, 'unit': 6579889036178736369039389120576021, 'val': 1}
  • id: 2900723
    {'lmfdb_iso': '57222.z', 'p': 67, 'prec': 20, 'unit': 13646997295921517429259267977386413, 'val': 1}
  • id: 2900738
    {'lmfdb_iso': '57222.z', 'p': 71, 'prec': 20, 'unit': 54288802848184600136644741905880745, 'val': 1}
  • id: 2900735
    {'lmfdb_iso': '57222.z', 'p': 73, 'prec': 20, 'unit': 11954080181160518940368573329442958, 'val': 1}
  • id: 2900731
    {'lmfdb_iso': '57222.z', 'p': 79, 'prec': 20, 'unit': 706514435323206267066611733340655224, 'val': 1}
  • id: 2900722
    {'lmfdb_iso': '57222.z', 'p': 83, 'prec': 20, 'unit': 1577026032610435930856849767425999935, 'val': 1}
  • id: 2900737
    {'lmfdb_iso': '57222.z', 'p': 89, 'prec': 20, 'unit': 9953755629132540935273950253962426719, 'val': 1}
  • id: 2900721
    {'lmfdb_iso': '57222.z', 'p': 97, 'prec': 20, 'unit': 29782410641758289994615657451844961738, 'val': 1}