Elliptic curve data - 9702.g1

Formats: - HTML - YAML - JSON - 2023-10-03T06:36:36.441090

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '9702s', 'Clabel': '9702s2', 'Cnumber': 2, 'absD': 22012410332850182784, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [1, -1, 0, -23134428, 42834024400], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9702, 'degree': 602112, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8443866286854743245926009690', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [46546832455691959, 748268928], 'lmfdb_iso': '9702.g', 'lmfdb_label': '9702.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -52459, 4620209], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '88.6.0.?', '616.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.0014931708208247145605093946', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.83564787255993450006596379296', 'prec': 103}, '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, -2, 0, 0, -1, 0, 2, -1, 0, 4, 0, 0, 1, -6, 0, 2, -2], 'aplist': [-1, 0, -2, 0, -1, 4, -6, 2, 0, 6, 2, 2, 2, -12, 6, -10, -8, 4, 0, 8, 6, 12, -6, 12, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 9702, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9702.g', 'trace_hash': 728728703548248628}
• 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': '0.0033837414041517342913627161741', 'prec': 110}, 'conductor': 9702, 'gens': [[3111, 29506, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.0014931708208247145605093946', 'prec': 100}], 'lmfdb_label': '9702.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19661736686745814634244701830', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7532303027745618018282471397235153479', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[11075, -11075, 2]], 'xcoord_integral_points': [3111]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': 'a', '5': [5, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [5, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '9702.g1'}
• ec_torsion_growth •

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

  
  
  • id: 503795
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '9702.g1', 'torsion': [2, 2]}
  • id: 503796
    {'degree': 4, 'field': [1386, 0, 63, 0, 1], 'lmfdb_label': '9702.g1', 'torsion': [4]}
  • id: 503799
    {'degree': 8, 'field': [72, 36, -216, -228, 0, 30, 2, -1, 1], 'lmfdb_label': '9702.g1', 'torsion': [6]}
  • id: 503798
    {'degree': 8, 'field': [14641, 0, 11946, 0, 3050, 0, -54, 0, 1], 'lmfdb_label': '9702.g1', 'torsion': [2, 4]}
  • id: 503797
    {'degree': 8, 'field': [16192575, 1048572, -1032878, -31360, 15611, 80, -22, -4, 1], 'lmfdb_label': '9702.g1', 'torsion': [2, 4]}
  • id: 503801
    {'degree': 16, 'field': [-23316928, 168556864, 196356624, -58467008, -85716608, 25792128, 14340176, -5176976, -404400, 323608, -12056, -19080, 1088, 496, -39, -2, 1], 'lmfdb_label': '9702.g1', 'torsion': [2, 6]}
  • id: 503800
    {'degree': 16, 'field': [26523, 109116, 715995, 947394, 2244229, -881336, 498636, -366932, 133356, -55684, 16998, -5512, 1461, -188, 69, -2, 1], 'lmfdb_label': '9702.g1', '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: 204499
    {'conductor': 9702, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '9702.g1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 204500
    {'conductor': 9702, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '9702.g1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 204501
    {'conductor': 9702, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '9702.g1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 204502
    {'conductor': 9702, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9702.g1', 'prime': 11, '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: 1728149
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [613, 4, 612, 5], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 307, 0], [180, 1, 263, 0], [114, 1, 559, 0], [233, 386, 384, 231]], 'adelic_image': '616.12.0.?', 'conductor': 9702, 'lmfdb_label': '9702.g1', 'prime': 0}
  • id: 46973
    {'conductor': 9702, 'elladic_image': '2.3.0.1', 'lmfdb_label': '9702.g1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 407382
    {'lmfdb_iso': '9702.g', 'p': 5, 'prec': 20, 'unit': 2132010035804, 'val': 2}
  • id: 407388
    {'lmfdb_iso': '9702.g', 'p': 13, 'prec': 20, 'unit': 1142750854690293393497, 'val': 1}
  • id: 407390
    {'lmfdb_iso': '9702.g', 'p': 17, 'prec': 20, 'unit': 236763176529318240838090, 'val': 1}
  • id: 407391
    {'lmfdb_iso': '9702.g', 'p': 19, 'prec': 20, 'unit': 167979167711779010975673, 'val': 1}
  • id: 407387
    {'lmfdb_iso': '9702.g', 'p': 29, 'prec': 20, 'unit': 3756703029518457002151539, 'val': 3}
  • id: 407384
    {'lmfdb_iso': '9702.g', 'p': 31, 'prec': 20, 'unit': 2510655386072880817376204885, 'val': 1}
  • id: 407397
    {'lmfdb_iso': '9702.g', 'p': 37, 'prec': 20, 'unit': 499242394929065749875982603839, 'val': 1}
  • id: 407385
    {'lmfdb_iso': '9702.g', 'p': 41, 'prec': 20, 'unit': 3039293373661492862317313321427, 'val': 1}
  • id: 407386
    {'lmfdb_iso': '9702.g', 'p': 43, 'prec': 20, 'unit': 8681030641743719217603754953883, 'val': 1}
  • id: 407395
    {'lmfdb_iso': '9702.g', 'p': 47, 'prec': 20, 'unit': 38071623180926976970254080803411, 'val': 1}
  • id: 407392
    {'lmfdb_iso': '9702.g', 'p': 53, 'prec': 20, 'unit': 29666863585763452920981556546271, 'val': 1}
  • id: 407381
    {'lmfdb_iso': '9702.g', 'p': 59, 'prec': 20, 'unit': 957769647161260468886570051562476, 'val': 1}
  • id: 407396
    {'lmfdb_iso': '9702.g', 'p': 61, 'prec': 20, 'unit': 1998762513827915880247896716839156, 'val': 1}
  • id: 407383
    {'lmfdb_iso': '9702.g', 'p': 71, 'prec': 20, 'unit': 128740575262278028996382361389514766, 'val': 1}
  • id: 407393
    {'lmfdb_iso': '9702.g', 'p': 73, 'prec': 20, 'unit': 156049827951967174140936102339652424, 'val': 1}
  • id: 407389
    {'lmfdb_iso': '9702.g', 'p': 79, 'prec': 20, 'unit': 789384887010512013902193208942847673, 'val': 1}
  • id: 407380
    {'lmfdb_iso': '9702.g', 'p': 83, 'prec': 20, 'unit': 459489353326896941643763743319493397, 'val': 1}
  • id: 407394
    {'lmfdb_iso': '9702.g', 'p': 89, 'prec': 20, 'unit': 10051102003951449176015864907930227503, 'val': 1}