Elliptic curve data - 72450.cs1

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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': '72450cm', 'Clabel': '72450cm1', 'Cnumber': 1, 'abc_quality': 1.041243552691389, 'absD': 71932167165950558208000000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 9660, 'ainvs': [1, -1, 1, -1108485380, 5939475630247], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 72450, 'degree': 74317824, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2310202747113474844278709526', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2], 'jinv': [489781415227546051766883, 233890092903563264000], 'lmfdb_iso': '72450.cs', 'lmfdb_label': '72450.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -44339415, 47524672925], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '210.6.0.?', '276.6.0.?', '3220.6.0.?', '9660.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.9903347500710822690117831628', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6023421019932150285810573583', 'prec': 100}, 'szpiro_ratio': 6.62091758117822, '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, -1, 1, 0, 0, -2, 0, 6, -1, 0, 1, -6, 0, 0, 0], 'aplist': [1, 0, 0, -1, -2, 6, -6, 0, 1, 4, -2, -4, 2, 4, 0, 6, 4, 0, -12, -8, 6, -8, -10, -2, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 72450, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '72450.cs', 'trace_hash': 913893694674355535}
• 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': '0.00021134037989005570939913910943', 'prec': 113}, 'conductor': 72450, 'gens': [[2053, 1915325, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.9903347500710822690117831628', 'prec': 100}], 'lmfdb_label': '72450.cs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.030820370650223333790114477072', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.8434538666163443040806094577036220794', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[5509, -2755, 1]], 'xcoord_integral_points': [2053, 5509, 299909]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [2, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '72450.cs1'}
• ec_torsion_growth •

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

  
  
  • id: 3435265
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '72450.cs1', 'torsion': [2, 2]}
  • id: 3435266
    {'degree': 4, 'field': [798, -138, 15, 0, 1], 'lmfdb_label': '72450.cs1', 'torsion': [4]}
  • id: 3435269
    {'degree': 8, 'field': [-12910, 20800, -8374, 1569, 0, 39, -17, -4, 1], 'lmfdb_label': '72450.cs1', 'torsion': [6]}
  • id: 3435268
    {'degree': 8, 'field': [6616, -40588, 17810, -2488, -71, 298, -40, -2, 1], 'lmfdb_label': '72450.cs1', 'torsion': [2, 4]}
  • id: 3435267
    {'degree': 8, 'field': [154336, -147392, 96352, -25208, 9478, -818, 67, -2, 1], 'lmfdb_label': '72450.cs1', 'torsion': [2, 4]}
  • id: 3435271
    {'degree': 16, 'field': [2928780, -7372260, 14785464, -17676096, 15162522, -5397744, -1712349, 2733600, -351110, -201338, 20527, 10180, -1181, -266, 58, -8, 1], 'lmfdb_label': '72450.cs1', 'torsion': [2, 6]}
  • id: 3435270
    {'degree': 16, 'field': [16320062500, 0, -73832275000, 0, 97368425000, 0, 16821147500, 0, 712751125, 0, 2769340, 0, 55334, 0, 136, 0, 1], 'lmfdb_label': '72450.cs1', '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: 1757473
    {'conductor': 72450, 'conductor_valuation': 1, 'discriminant_valuation': 32, 'j_denominator_valuation': 32, 'kodaira_symbol': 36, 'lmfdb_label': '72450.cs1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 32}
  • id: 1757474
    {'conductor': 72450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '72450.cs1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1757475
    {'conductor': 72450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '72450.cs1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1757476
    {'conductor': 72450, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '72450.cs1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1757477
    {'conductor': 72450, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '72450.cs1', 'prime': 23, '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: 2143002
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [6721, 4, 3782, 9], [3224, 1, 6439, 0], [1934, 1, 3863, 0], [1, 0, 4, 1], [3, 4, 8, 11], [9657, 4, 9656, 5], [5522, 1, 6899, 0], [7249, 2416, 7244, 2415]], 'adelic_image': '9660.12.0.?', 'conductor': 72450, 'lmfdb_label': '72450.cs1', 'prime': 0}
  • id: 300827
    {'conductor': 72450, 'elladic_image': '2.3.0.1', 'lmfdb_label': '72450.cs1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3718967
    {'lmfdb_iso': '72450.cs', 'p': 11, 'prec': 20, 'unit': 51828314683306880357, 'val': 1}
  • id: 3718972
    {'lmfdb_iso': '72450.cs', 'p': 13, 'prec': 20, 'unit': 636754400300122368458, 'val': 1}
  • id: 3718974
    {'lmfdb_iso': '72450.cs', 'p': 17, 'prec': 20, 'unit': 194416698996345002107204, 'val': 1}
  • id: 3718980
    {'lmfdb_iso': '72450.cs', 'p': 29, 'prec': 20, 'unit': 5976560131312771080155852112, 'val': 1}
  • id: 3718981
    {'lmfdb_iso': '72450.cs', 'p': 31, 'prec': 20, 'unit': 19889058629861505535687639532, 'val': 1}
  • id: 3718968
    {'lmfdb_iso': '72450.cs', 'p': 37, 'prec': 20, 'unit': 193594077836392032847894326119, 'val': 1}
  • id: 3718970
    {'lmfdb_iso': '72450.cs', 'p': 41, 'prec': 20, 'unit': 469385620552438213670073944415, 'val': 1}
  • id: 3718971
    {'lmfdb_iso': '72450.cs', 'p': 43, 'prec': 20, 'unit': 6143501746389082430606594384693, 'val': 1}
  • id: 3718976
    {'lmfdb_iso': '72450.cs', 'p': 53, 'prec': 20, 'unit': 141398564212213408510822215924115, 'val': 1}
  • id: 3718979
    {'lmfdb_iso': '72450.cs', 'p': 59, 'prec': 20, 'unit': 2743449442593361742386748823706996, 'val': 1}
  • id: 3718966
    {'lmfdb_iso': '72450.cs', 'p': 67, 'prec': 20, 'unit': 48208915179608188119772334235409702, 'val': 1}
  • id: 3718969
    {'lmfdb_iso': '72450.cs', 'p': 71, 'prec': 20, 'unit': 120976287530414003109889877231414190, 'val': 1}
  • id: 3718977
    {'lmfdb_iso': '72450.cs', 'p': 73, 'prec': 20, 'unit': 233226070664722315497801533523972631, 'val': 1}
  • id: 3718973
    {'lmfdb_iso': '72450.cs', 'p': 79, 'prec': 20, 'unit': 380509368025502854483226538752643761, 'val': 1}
  • id: 3718975
    {'lmfdb_iso': '72450.cs', 'p': 83, 'prec': 20, 'unit': 1360241401232928796203171089860271906, 'val': 1}
  • id: 3718978
    {'lmfdb_iso': '72450.cs', 'p': 89, 'prec': 20, 'unit': 3801751231150024819268406293082641289, 'val': 1}
  • id: 3718965
    {'lmfdb_iso': '72450.cs', 'p': 97, 'prec': 20, 'unit': 47748928399900955206003087027130201121, 'val': 1}