Elliptic curve data - 211185.s2

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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': '211185q', 'Clabel': '211185q2', 'Cnumber': 2, 'abc_quality': 1.001928731766074, 'absD': 10172154771817155, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 7410, 'ainvs': [0, 0, 1, 38988, -3842755], 'analytic_rank': 1, 'bad_primes': [3, 5, 13, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 211185, 'degree': 995328, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7568110204586962747335390482', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [7077888, 10985], 'lmfdb_iso': '211185.s', 'lmfdb_label': '211185.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 12, -21], 'min_quad_twist_disc': 57, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '57.8.0-3.a.1.2', '390.8.0.?', '7410.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.8779214269459564596434273995', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 70395], [3, 2, 1805], [5, 6, 42237], [13, 14, 16245], [19, 182, 585]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53936768562560622381740859544', 'prec': 107}, 'szpiro_ratio': 3.57624746917272, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, -2, 1, 0, -1, 0, 0, 0, -3, 0, -1, 0, 0, 4, -3, 0, 0, -2], 'aplist': [0, 0, 1, -1, -3, -1, -3, 0, -9, 6, -2, 1, 3, 2, -6, -9, 12, 5, 4, -9, 14, 7, 0, -15, -5], 'class_deg': 3, 'class_size': 2, 'conductor': 211185, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '211185.s', 'trace_hash': 2184678435579013133}
• 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': '0.029788822464478655577969144157', 'prec': 107}, 'conductor': 211185, 'gens': [[9861, 1067234, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '4.8779214269459564596434273995', 'prec': 100}], 'lmfdb_label': '211185.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21505095334357808929900578786', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1960066127991789590543866740449365779', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 211185.s2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9226607
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '211185.s2', 'torsion': [3]}
  • id: 9226608
    {'degree': 3, 'field': [-5, -1, -1, 1], 'lmfdb_label': '211185.s2', 'torsion': [2]}
  • id: 9226611
    {'degree': 6, 'field': [-2406, 246, 598, 41, -45, -1, 1], 'lmfdb_label': '211185.s2', 'torsion': [6]}
  • id: 9226610
    {'degree': 6, 'field': [220, -210, 75, -21, 18, -3, 1], 'lmfdb_label': '211185.s2', 'torsion': [3]}
  • id: 9226609
    {'degree': 6, 'field': [780, 0, 16, 0, -8, 0, 1], 'lmfdb_label': '211185.s2', 'torsion': [2, 2]}
  • id: 9226612
    {'degree': 12, 'field': [-356689002632, 66943380848, 36075072336, -5206635416, -1297615988, 86788560, 20972392, 176712, -66966, -988, -8, -6, 1], 'lmfdb_label': '211185.s2', 'torsion': [4]}
  • id: 9226613
    {'degree': 12, 'field': [48400, -46200, 27600, -6510, -2745, 5325, -1099, -138, 186, -12, -9, -3, 1], 'lmfdb_label': '211185.s2', 'torsion': [3, 3]}
  • id: 9226614
    {'degree': 12, 'field': [6555111, -5512635, 2819647, -1193136, 412663, -148829, 67288, -16109, 2077, -104, 13, -3, 1], 'lmfdb_label': '211185.s2', 'torsion': [2, 6]}
  • id: 9226615
    {'degree': 18, 'field': [-54384288119, -58041102609, 54750674529, 23022410340, -11942802459, -5247073800, 1507864632, 661720347, -127961604, -50586266, 7633710, 2502783, -328377, -78111, 9711, 1326, -162, -9, 1], 'lmfdb_label': '211185.s2', 'torsion': [9]}
  • id: 9226616
    {'degree': 18, 'field': [48193820, 49568340, 33220860, -18346156, -7784292, -903444, 6236419, -3777003, 1560471, -485880, 160635, -23235, 7250, -741, 573, -34, 39, -3, 1], 'lmfdb_label': '211185.s2', 'torsion': [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: 5234051
    {'conductor': 211185, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '211185.s2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5234052
    {'conductor': 211185, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '211185.s2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5234053
    {'conductor': 211185, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '211185.s2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5234054
    {'conductor': 211185, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '211185.s2', 'prime': 19, 'reduction_type': 0, '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: 3014982
    {'adelic_gens': [[4, 3, 9, 7], [6174, 5909, 7277, 5376], [7405, 6, 7404, 7], [3421, 2736, 513, 799], [6629, 0, 0, 7409], [4447, 2736, 3591, 799], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '7410.16.0.?', 'conductor': 211185, 'lmfdb_label': '211185.s2', 'prime': 0}
  • id: 778753
    {'conductor': 211185, 'elladic_image': '3.4.0.1', 'lmfdb_label': '211185.s2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 211185.s does not appear in ec_padic