Elliptic curve data - 7744.v1

Formats: - HTML - YAML - JSON - 2024-05-15T02:19:18.815436

• 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': '7744t', 'Clabel': '7744t3', 'Cnumber': 3, 'abc_quality': 1.172456969504371, 'absD': 58050510848, 'ainvs': [0, 0, 0, -5324, -149072], 'analytic_rank': 1, 'bad_primes': [2, 11], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 7744, 'degree': 5760, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.92813548132759371790454488787', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '7744.v', 'lmfdb_label': '7744.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': 88, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.5062899407788236680130158830', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, 'szpiro_ratio': 4.171402009614269, '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, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 2, 0, 0, 6, -2, 0, 0, -10, 0, 2, -10, 0, 0, -14, 0, -10, 0, 0, 6, 0, 0, 10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 7744, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '7744.v', 'trace_hash': 1877043300475719057}
• 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': '0.15625422313682665517022944954', 'prec': 103}, 'conductor': 7744, 'gens': [[-9851, 33607, 15]], 'heights': [{'__RealLiteral__': 0, 'data': '8.5062899407788236680130158830', 'prec': 100}], 'lmfdb_label': '7744.v1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.55902454890071984238620829278', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7552248969626128037323693892320056359', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-44, 0, 1]], 'xcoord_integral_points': [-44]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [3, 0], '7': [7, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '7744.v1'}
• ec_torsion_growth •

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

  
  
  • id: 405242
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 2]}
  • id: 405244
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '7744.v1', 'torsion': [4]}
  • id: 405243
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [4]}
  • id: 405245
    {'degree': 4, 'field': [23, -2, 3, -2, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 4]}
  • id: 405249
    {'degree': 8, 'field': [-43923, 0, 0, 0, -726, 0, 0, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [6]}
  • id: 405246
    {'degree': 8, 'field': [49, 0, -148, 0, -76, 0, -4, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 4]}
  • id: 405248
    {'degree': 8, 'field': [463, -172, 218, -96, 59, -16, 10, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 8]}
  • id: 405247
    {'degree': 8, 'field': [746, -864, 932, -480, 294, -80, 32, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [8]}
  • id: 405250
    {'degree': 8, 'field': [18362, -7008, 1596, -1100, 496, -24, -22, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [10]}
  • id: 405252
    {'degree': 16, 'field': [521, -2044, 2452, 3412, -8540, -784, 11104, -1932, -6779, 2040, 2012, -852, -222, 140, 0, -8, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 8]}
  • id: 405259
    {'degree': 16, 'field': [6549, -33816, 70872, -97176, 113562, -100008, 74988, -46320, 26683, -13112, 6028, -2336, 814, -224, 52, -8, 1], 'lmfdb_label': '7744.v1', 'torsion': [12]}
  • id: 405251
    {'degree': 16, 'field': [6561, 0, -14580, 0, 16200, 0, -12600, 0, 6079, 0, -1400, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [4, 4]}
  • id: 405260
    {'degree': 16, 'field': [164025, 0, 0, 0, 5670, 0, 0, 0, -241, 0, 0, 0, 14, 0, 0, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [20]}
  • id: 405255
    {'degree': 16, 'field': [287422, 304584, 515396, 494400, 350152, 255912, 111716, 64008, 17524, 5388, -1336, -552, -386, -72, -4, 0, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 6]}
  • id: 405258
    {'degree': 16, 'field': [905546, -692304, 1480748, -847864, 1001580, -468240, 386612, -145672, 91240, -26668, 13152, -2840, 1122, -164, 52, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [20]}
  • id: 405256
    {'degree': 16, 'field': [1429921, 1593188, -955844, -1566944, 223582, 704992, -18720, -187632, 940, 31580, -444, -3496, 202, 200, -12, -8, 1], 'lmfdb_label': '7744.v1', 'torsion': [2, 10]}
  • id: 405257
    {'degree': 16, 'field': [2673961, -42356, 2746916, -437652, 1316342, -323632, 394216, -108228, 79516, -20388, 10660, -2276, 902, -144, 44, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [12]}
  • id: 405254
    {'degree': 16, 'field': [7616156, 26984048, 36890824, 31016336, 12765016, 6602744, 1407280, 420680, 31442, -11920, -4140, -2092, -44, -92, 26, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [10]}
  • id: 405253
    {'degree': 16, 'field': [182277577, 21590704, 53809544, -20998908, 11491220, -8173024, 2861590, -1349436, 432247, -139104, 37834, -8600, 2162, -276, 74, -4, 1], 'lmfdb_label': '7744.v1', 'torsion': [3, 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: 159896
    {'conductor': 7744, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '7744.v1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 159897
    {'conductor': 7744, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7744.v1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 7744.v1 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 316206
    {'lmfdb_iso': '7744.v', 'p': 5, 'prec': 20, 'unit': 975314696321, 'val': 2}
  • id: 316199
    {'lmfdb_iso': '7744.v', 'p': 13, 'prec': 20, 'unit': 406719949732863188843, 'val': 1}
  • id: 316201
    {'lmfdb_iso': '7744.v', 'p': 17, 'prec': 20, 'unit': 215999421790838360581494, 'val': 1}
  • id: 316200
    {'lmfdb_iso': '7744.v', 'p': 29, 'prec': 20, 'unit': 2282545988805077752168491063, 'val': 1}
  • id: 316197
    {'lmfdb_iso': '7744.v', 'p': 37, 'prec': 20, 'unit': 290268518406595624683502457822, 'val': 1}
  • id: 316198
    {'lmfdb_iso': '7744.v', 'p': 41, 'prec': 20, 'unit': 3422452083375411326804227622515, 'val': 1}
  • id: 316202
    {'lmfdb_iso': '7744.v', 'p': 53, 'prec': 20, 'unit': 386835354092612268009833322508862, 'val': 1}
  • id: 316205
    {'lmfdb_iso': '7744.v', 'p': 61, 'prec': 20, 'unit': 2297057131429429841761985436982642, 'val': 1}
  • id: 316203
    {'lmfdb_iso': '7744.v', 'p': 73, 'prec': 20, 'unit': 244174819539709847955010540454058928, 'val': 1}
  • id: 316204
    {'lmfdb_iso': '7744.v', 'p': 89, 'prec': 20, 'unit': 8992156699224542197806940532095980664, 'val': 1}
  • id: 316196
    {'lmfdb_iso': '7744.v', 'p': 97, 'prec': 20, 'unit': 15916104547527280704219610827397204501, 'val': 1}