Elliptic curve data - 78144.s3

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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': '78144d', 'Clabel': '78144d2', 'Cnumber': 2, 'abc_quality': 1.0214304364495703, 'absD': 801687771700789248, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9768, 'ainvs': [0, -1, 0, -856193, -301590399], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 37], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 78144, 'degree': 1327104, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2481682597983721227778195887', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [264788619837198625, 3058196150592], 'lmfdb_iso': '78144.s', 'lmfdb_label': '78144.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -13378, -590716], 'min_quad_twist_disc': 8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.11', '74.6.0.?', '132.24.0.?', '222.24.0.?', '264.48.0.?', '888.48.0.?', '4884.48.1.?', '9768.96.1.?'], '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': '10.349832000682871299927303713', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 37], [3, 4, 2368], [11, 12, 7104], [37, 38, 2112]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2084474889584541586519714065', 'prec': 100}, 'szpiro_ratio': 4.66828661964966, '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, 0, -1, 0, 0, 0, -4, 0, 1, 0, -1, 0, 4, 0, 0, 0, -6, 0, -2, 0], 'aplist': [0, -1, 0, -4, -1, 4, -6, -2, -6, 6, -4, -1, 6, -2, 0, -6, -6, -8, 4, -12, 2, 2, 12, 0, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 78144, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '78144.s', 'trace_hash': 22756171792703621}
• 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': '0.011149768767891519436101856746', 'prec': 107}, 'conductor': 78144, 'gens': [[-84057, 2163864, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '10.349832000682871299927303713', 'prec': 100}], 'lmfdb_label': '78144.s3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15705789555058244392739544065', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2510456666586522521928718633803249980', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-577, 0, 1]], 'xcoord_integral_points': [-577]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '78144.s3'}
• ec_torsion_growth •

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

  
  
  • id: 3688070
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 2]}
  • id: 3688071
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [6]}
  • id: 3688073
    {'degree': 4, 'field': [47, 22, -21, -2, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 6]}
  • id: 3688072
    {'degree': 4, 'field': [592, 0, 50, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [4]}
  • id: 3688074
    {'degree': 6, 'field': [384, 0, 100, 0, 2, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [6]}
  • id: 3688076
    {'degree': 8, 'field': [1296, 0, 2664, 0, 1408, 0, 74, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 4]}
  • id: 3688077
    {'degree': 8, 'field': [10404, 0, 948, 0, 253, 0, 8, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [12]}
  • id: 3688075
    {'degree': 8, 'field': [1159929, 0, -192220, 0, 7646, 0, -140, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 4]}
  • id: 3688078
    {'degree': 12, 'field': [2428, 9072, 10718, 2544, -2109, -168, 70, -360, 81, -12, 8, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [3, 6]}
  • id: 3688079
    {'degree': 12, 'field': [64009, 0, 6696, 0, 26100, 0, 4246, 0, 540, 0, 36, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 6]}
  • id: 3688081
    {'degree': 16, 'field': [813572, 499176, -924436, 930880, -664446, 230468, -53312, -40908, 39451, -24176, 8804, -1260, -518, 308, -24, -8, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 12]}
  • id: 3688082
    {'degree': 16, 'field': [6086089, 0, -4777778, 0, 2414597, 0, -442566, 0, 42164, 0, 15318, 0, 1445, 0, 58, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [2, 12]}
  • id: 3688080
    {'degree': 16, 'field': [80252090944, 0, -10003266240, 0, 779274928, 0, -19689120, 0, -608820, 0, 74580, 0, 2293, 0, 0, 0, 1], 'lmfdb_label': '78144.s3', 'torsion': [8]}
  • id: 3688083
    {'degree': 18, 'field': [-142569265088, -199687793664, 149984557248, 213295686272, -62137969488, -66141622752, 9838370688, 4194109248, 828402852, -54159984, -10493448, -2499144, 202575, 44322, 5751, -476, -51, -6, 1], 'lmfdb_label': '78144.s3', '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: 1901220
    {'conductor': 78144, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '78144.s3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1901221
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '78144.s3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1901222
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '78144.s3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1901223
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '78144.s3', 'prime': 37, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2180014
    {'adelic_gens': [[4895, 9756, 4896, 9755], [9757, 9766, 4934, 4893], [8131, 9766, 8136, 9767], [8435, 9756, 6654, 9695], [11, 2, 9718, 9759], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [9757, 12, 9756, 13], [2859, 4480, 2822, 4469], [538, 3, 501, 4876], [4883, 0, 0, 9767]], 'adelic_image': '9768.96.1.?', 'conductor': 78144, 'lmfdb_label': '78144.s3', 'prime': 0}
  • id: 322196
    {'conductor': 78144, 'elladic_image': '2.3.0.1', 'lmfdb_label': '78144.s3', 'modell_image': '2B', 'prime': 2}
  • id: 322197
    {'conductor': 78144, 'elladic_image': '3.4.0.1', 'lmfdb_label': '78144.s3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 4023104
    {'lmfdb_iso': '78144.s', 'p': 7, 'prec': 20, 'unit': 11283646424964740, 'val': 1}
  • id: 4023108
    {'lmfdb_iso': '78144.s', 'p': 13, 'prec': 20, 'unit': 992672132193251504071, 'val': 1}
  • id: 4023110
    {'lmfdb_iso': '78144.s', 'p': 17, 'prec': 20, 'unit': 117173803969626747559627, 'val': 1}
  • id: 4023101
    {'lmfdb_iso': '78144.s', 'p': 19, 'prec': 20, 'unit': 423925405309152053821636, 'val': 1}
  • id: 4023114
    {'lmfdb_iso': '78144.s', 'p': 23, 'prec': 20, 'unit': 34403546643748894567335024, 'val': 1}
  • id: 4023107
    {'lmfdb_iso': '78144.s', 'p': 29, 'prec': 20, 'unit': 1615181227228599962498365847, 'val': 1}
  • id: 4023118
    {'lmfdb_iso': '78144.s', 'p': 31, 'prec': 20, 'unit': 218668747375268731314814609, 'val': 1}
  • id: 4023105
    {'lmfdb_iso': '78144.s', 'p': 41, 'prec': 20, 'unit': 1527333222031255726618069364175, 'val': 1}
  • id: 4023106
    {'lmfdb_iso': '78144.s', 'p': 43, 'prec': 20, 'unit': 3447351614080554683591250427866, 'val': 1}
  • id: 4023112
    {'lmfdb_iso': '78144.s', 'p': 53, 'prec': 20, 'unit': 568947024145025923091849297816204, 'val': 1}
  • id: 4023116
    {'lmfdb_iso': '78144.s', 'p': 59, 'prec': 20, 'unit': 645097490167310698012114733348996, 'val': 1}
  • id: 4023117
    {'lmfdb_iso': '78144.s', 'p': 61, 'prec': 20, 'unit': 7427753759527804133947250418195962, 'val': 1}
  • id: 4023103
    {'lmfdb_iso': '78144.s', 'p': 67, 'prec': 20, 'unit': 21143485548889676939607503810670341, 'val': 1}
  • id: 4023115
    {'lmfdb_iso': '78144.s', 'p': 71, 'prec': 20, 'unit': 146074094069151140156009288539500676, 'val': 1}
  • id: 4023113
    {'lmfdb_iso': '78144.s', 'p': 73, 'prec': 20, 'unit': 114344469126927024231260816706195278, 'val': 1}
  • id: 4023109
    {'lmfdb_iso': '78144.s', 'p': 79, 'prec': 20, 'unit': 686918932167148537509260264155534858, 'val': 1}
  • id: 4023111
    {'lmfdb_iso': '78144.s', 'p': 83, 'prec': 20, 'unit': 1847151505028000737277695689828939034, 'val': 1}
  • id: 4023102
    {'lmfdb_iso': '78144.s', 'p': 97, 'prec': 20, 'unit': 22484134233387199843794516966468858310, 'val': 1}