Elliptic curve data - 49725.h2

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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': '49725m', 'Clabel': '49725m2', 'Cnumber': 2, 'abc_quality': 0.8551938712460835, 'absD': 125174141015625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8840, 'ainvs': [1, -1, 1, 5620, 511872], 'analytic_rank': 1, 'bad_primes': [3, 5, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 49725, 'degree': 122880, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3868574462688102438692667743', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2], 'jinv': [1723683599, 10989225], 'lmfdb_iso': '49725.h', 'lmfdb_label': '49725.h2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 25, -150], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '40.12.0-4.a.1.1', '1768.12.0.?', '4420.12.0.?', '8840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2069208054570562231711460505', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 8, 5525], [5, 18, 1989], [13, 14, 3825], [17, 18, 2925]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.032832345717705210871264489226', 'prec': 107}, 'szpiro_ratio': 3.6822008466036578, '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, 2, 3, 0, 0, 0, 0, 1, -2, 0, -1, -1, 0, 2, 0], 'aplist': [-1, 0, 0, 2, 0, 1, -1, 2, 0, 10, -4, -2, -6, -6, -8, -2, -10, 10, 8, 12, 6, -14, 16, 10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 49725, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '49725.h', 'trace_hash': 584423542473821142}
• 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': '0.062429653974621974083620394262', 'prec': 107}, 'conductor': 49725, 'gens': [[24, 800, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2069208054570562231711460505', 'prec': 100}], 'lmfdb_label': '49725.h2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42574901324090578572337978188', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1107627358660872467611974665166406510', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-229, 225, 2]], 'xcoord_integral_points': [-27, 24, 134]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '49725.h2'}
• ec_torsion_growth •

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

  
  
  • id: 2417784
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [2, 2]}
  • id: 2417785
    {'degree': 4, 'field': [-36, 0, -99, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [4]}
  • id: 2417788
    {'degree': 8, 'field': [-721461, -282906, -109785, -24363, -2565, -198, -68, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [6]}
  • id: 2417786
    {'degree': 8, 'field': [336400, 0, -47520, 0, 2801, 0, -72, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [2, 4]}
  • id: 2417787
    {'degree': 8, 'field': [6031936, -54032, 242, -10022, 4993, 14, 8, -4, 1], 'lmfdb_label': '49725.h2', 'torsion': [2, 4]}
  • id: 2417789
    {'degree': 16, 'field': [3662186256, 0, 0, 0, 862568937, 0, 0, 0, -267677, 0, 0, 0, 3467, 0, 0, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [4, 4]}
  • id: 2417791
    {'degree': 16, 'field': [520505974521, 0, -78375386934, 0, 1968963399, 0, 44270799, 0, 10419315, 0, -90066, 0, -506, 0, 136, 0, 1], 'lmfdb_label': '49725.h2', 'torsion': [2, 6]}
  • id: 2417790
    {'degree': 16, 'field': [767544201216, 0, 59588545536, 0, -7946677440, 0, -1208603136, 0, 2650924, 0, 2745804, 0, 30955, 0, -324, 0, 1], 'lmfdb_label': '49725.h2', '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: 1189524
    {'conductor': 49725, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '49725.h2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1189525
    {'conductor': 49725, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '49725.h2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1189526
    {'conductor': 49725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49725.h2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1189527
    {'conductor': 49725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49725.h2', 'prime': 17, '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: 1994986
    {'adelic_gens': [[1, 8, 0, 1], [8833, 8, 8832, 9], [6801, 6, 0, 1], [6631, 8, 5527, 17], [8839, 8832, 8838, 8823], [1, 0, 8, 1], [5, 8, 48, 77], [3, 8, 10, 27], [3641, 6, 0, 1], [5303, 8834, 0, 8839], [4421, 8, 2, 17]], 'adelic_image': '8840.48.0.?', 'conductor': 49725, 'lmfdb_label': '49725.h2', 'prime': 0}
  • id: 213966
    {'conductor': 49725, 'elladic_image': '4.6.0.5', 'lmfdb_label': '49725.h2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2498421
    {'lmfdb_iso': '49725.h', 'p': 7, 'prec': 20, 'unit': 10707055043442250, 'val': 1}
  • id: 2498417
    {'lmfdb_iso': '49725.h', 'p': 19, 'prec': 20, 'unit': 92403124954546649406029, 'val': 1}
  • id: 2498424
    {'lmfdb_iso': '49725.h', 'p': 29, 'prec': 20, 'unit': 4818088157227811709676788245, 'val': 1}
  • id: 2498434
    {'lmfdb_iso': '49725.h', 'p': 31, 'prec': 20, 'unit': 2854195740608294084204544851, 'val': 1}
  • id: 2498420
    {'lmfdb_iso': '49725.h', 'p': 37, 'prec': 20, 'unit': 314621305600133313694061007980, 'val': 1}
  • id: 2498422
    {'lmfdb_iso': '49725.h', 'p': 41, 'prec': 20, 'unit': 2517600106207462787754106784008, 'val': 1}
  • id: 2498423
    {'lmfdb_iso': '49725.h', 'p': 43, 'prec': 20, 'unit': 5719175977988228678655979597895, 'val': 1}
  • id: 2498432
    {'lmfdb_iso': '49725.h', 'p': 47, 'prec': 20, 'unit': 31120468829597034961831814247636, 'val': 1}
  • id: 2498428
    {'lmfdb_iso': '49725.h', 'p': 53, 'prec': 20, 'unit': 313900059470816374401094911299932, 'val': 1}
  • id: 2498426
    {'lmfdb_iso': '49725.h', 'p': 59, 'prec': 20, 'unit': 3469650494432001930761461783596562, 'val': 1}
  • id: 2498433
    {'lmfdb_iso': '49725.h', 'p': 61, 'prec': 20, 'unit': 565965932696361534488941247779313, 'val': 1}
  • id: 2498419
    {'lmfdb_iso': '49725.h', 'p': 67, 'prec': 20, 'unit': 3044727926769974720727816222565788, 'val': 1}
  • id: 2498431
    {'lmfdb_iso': '49725.h', 'p': 71, 'prec': 20, 'unit': 1222290887364298706592238700115401, 'val': 1}
  • id: 2498429
    {'lmfdb_iso': '49725.h', 'p': 73, 'prec': 20, 'unit': 55224332063499862754441815557605120, 'val': 1}
  • id: 2498425
    {'lmfdb_iso': '49725.h', 'p': 79, 'prec': 20, 'unit': 126587623070356409135806466191885190, 'val': 1}
  • id: 2498427
    {'lmfdb_iso': '49725.h', 'p': 83, 'prec': 20, 'unit': 1426276785815467316111577333221605596, 'val': 1}
  • id: 2498430
    {'lmfdb_iso': '49725.h', 'p': 89, 'prec': 20, 'unit': 7070550166314255876809725517277516241, 'val': 1}
  • id: 2498418
    {'lmfdb_iso': '49725.h', 'p': 97, 'prec': 20, 'unit': 2477924567293189602271019445023825449, 'val': 1}