Elliptic curve data - 71148.z1

Formats: - HTML - YAML - JSON - 2024-05-05T03:44:21.410728

• 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': '71148f', 'Clabel': '71148f1', 'Cnumber': 1, 'abc_quality': 1.0627761835505283, 'absD': 222339890857392, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6, 'ainvs': [0, -1, 0, -173917, 27983782], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 71148, 'degree': 441936, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7189100258326534460829512760', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1], 'jinv': [-70647808, 27], 'lmfdb_iso': '71148.z', 'lmfdb_label': '71148.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1437, -20502], 'min_quad_twist_disc': -11, 'modell_images': [], 'modm_images': ['6.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9724685267650801722667992649', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.75937259923801312146587273094', 'prec': 107}, 'szpiro_ratio': 4.279543026341058, '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, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 5, 0, -2, 0, -6, 0, 4, 0], 'aplist': [0, -1, 2, 0, 0, 5, -6, 4, -2, -10, 5, 3, 6, -1, -2, 4, -8, -5, -4, 2, -11, 16, -8, 4, 9], 'class_deg': 1, 'class_size': 1, 'conductor': 71148, 'isogeny_matrix': [[1]], 'lmfdb_iso': '71148.z', 'trace_hash': 1846068879252457864}
• 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': '0.032134660929130071567448912403', 'prec': 107}, 'conductor': 71148, 'gens': [[233, 237, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.9724685267650801722667992649', 'prec': 100}], 'lmfdb_label': '71148.z1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.54983177163055765669806936314', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5525682234536261328547803449122165834', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [233]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': 'a', '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, 0]}, 'iwp0': 0, 'lmfdb_label': '71148.z1'}
• ec_torsion_growth •

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

  
  
  • id: 3379518
    {'degree': 3, 'field': [-20, 26, -1, 1], 'lmfdb_label': '71148.z1', 'torsion': [2]}
  • id: 3379519
    {'degree': 6, 'field': [400, -520, 656, 14, -25, -1, 1], 'lmfdb_label': '71148.z1', 'torsion': [2, 2]}
  • id: 3379520
    {'degree': 8, 'field': [-34, 133, -136, 5, 1, -7, 7, -4, 1], 'lmfdb_label': '71148.z1', 'torsion': [3]}
  • id: 3379521
    {'degree': 12, 'field': [-861888, 0, 346112, 0, -38016, 0, -2048, 0, 704, 0, -48, 0, 1], 'lmfdb_label': '71148.z1', 'torsion': [4]}
• 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: 1725675
    {'conductor': 71148, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '71148.z1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1725676
    {'conductor': 71148, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '71148.z1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1725677
    {'conductor': 71148, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '71148.z1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1725678
    {'conductor': 71148, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '71148.z1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 5, 0], [1, 2, 0, 1], [5, 2, 4, 3], [1, 0, 2, 1]], 'adelic_image': '6.2.0.?', 'conductor': 71148, 'lmfdb_label': '71148.z1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 3653167
    {'lmfdb_iso': '71148.z', 'p': 5, 'prec': 20, 'unit': 5856230384214, 'val': 1}
  • id: 3653173
    {'lmfdb_iso': '71148.z', 'p': 13, 'prec': 20, 'unit': 81045521852024785241, 'val': 1}
  • id: 3653175
    {'lmfdb_iso': '71148.z', 'p': 17, 'prec': 20, 'unit': 147940422526802309557454, 'val': 1}
  • id: 3653176
    {'lmfdb_iso': '71148.z', 'p': 19, 'prec': 20, 'unit': 1620046382178914435397470, 'val': 1}
  • id: 3653180
    {'lmfdb_iso': '71148.z', 'p': 23, 'prec': 20, 'unit': 21932979241627934533185086, 'val': 1}
  • id: 3653172
    {'lmfdb_iso': '71148.z', 'p': 29, 'prec': 20, 'unit': 5600248993144439478985479487, 'val': 1}
  • id: 3653169
    {'lmfdb_iso': '71148.z', 'p': 31, 'prec': 20, 'unit': 17818850899147569903053197128, 'val': 1}
  • id: 3653184
    {'lmfdb_iso': '71148.z', 'p': 37, 'prec': 20, 'unit': 5187272185883754091692776826, 'val': 1}
  • id: 3653170
    {'lmfdb_iso': '71148.z', 'p': 41, 'prec': 20, 'unit': 3312170012133854668643426485152, 'val': 1}
  • id: 3653171
    {'lmfdb_iso': '71148.z', 'p': 43, 'prec': 20, 'unit': 4508885207802604086254567036252, 'val': 1}
  • id: 3653182
    {'lmfdb_iso': '71148.z', 'p': 47, 'prec': 20, 'unit': 39529878427991561704638049322450, 'val': 1}
  • id: 3653177
    {'lmfdb_iso': '71148.z', 'p': 53, 'prec': 20, 'unit': 227639588164771657728320949100283, 'val': 1}
  • id: 3653178
    {'lmfdb_iso': '71148.z', 'p': 59, 'prec': 20, 'unit': 2741598836345962963042813843435820, 'val': 1}
  • id: 3653183
    {'lmfdb_iso': '71148.z', 'p': 61, 'prec': 20, 'unit': 4902197030449873333161053866473548, 'val': 1}
  • id: 3653166
    {'lmfdb_iso': '71148.z', 'p': 67, 'prec': 20, 'unit': 17916520059998457594275623236998055, 'val': 1}
  • id: 3653168
    {'lmfdb_iso': '71148.z', 'p': 71, 'prec': 20, 'unit': 17647563718349998339418907416194730, 'val': 1}
  • id: 3653179
    {'lmfdb_iso': '71148.z', 'p': 73, 'prec': 20, 'unit': 57486848725842348121859563385370198, 'val': 1}
  • id: 3653174
    {'lmfdb_iso': '71148.z', 'p': 79, 'prec': 20, 'unit': 113972774284757328416889824601465390, 'val': 1}
  • id: 3653165
    {'lmfdb_iso': '71148.z', 'p': 83, 'prec': 20, 'unit': 1409057119020911115034762576458341902, 'val': 1}
  • id: 3653181
    {'lmfdb_iso': '71148.z', 'p': 89, 'prec': 20, 'unit': 9029272056013949857806911522251976592, 'val': 1}
  • id: 3653164
    {'lmfdb_iso': '71148.z', 'p': 97, 'prec': 20, 'unit': 522700357638790445632429717288855985, 'val': 1}