Elliptic curve data - 27075.f1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '27075g', 'Clabel': '27075g8', 'Cnumber': 8, 'abc_quality': 1.0735374703334082, 'absD': 297712215703125, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 9120, 'ainvs': [1, 1, 1, -19494188, 33120687656], 'analytic_rank': 2, 'bad_primes': [3, 5, 19], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 27075, 'degree': 663552, 'elladic_images': ['16.48.0.121'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5678080542773719392785290068', 'prec': 97}, 'faltings_index': 6, 'faltings_ratio': 16, 'intrinsic_torsion': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1114544804970241, 405], 'lmfdb_iso': '27075.f', 'lmfdb_label': '27075.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -2160, -39540], 'min_quad_twist_disc': -95, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '10.6.0.a.1', '16.48.0.x.2', '20.12.0.g.1', '40.48.0.bj.1', '76.12.0.?', '80.96.1.?', '96.96.1.?', '152.48.0.?', '160.192.5.?', '240.192.5.?', '304.96.0.?', '380.24.0.?', '480.384.13.?', '760.96.0.?', '1520.192.1.?', '1824.192.1.?', '3040.384.5.?', '4560.384.5.?', '9120.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 16, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.7143762077620004965780447012', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 9025], [3, 4, 9025], [5, 18, 1083], [19, 182, 75]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562424', 'prec': 97}, 'szpiro_ratio': 6.071748101433514, '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, -1, -1, 0, 1, 0, 3, 1, 0, -4, 1, -2, 0, 0, -1, -2, -1, 0, 0], 'aplist': [-1, -1, 0, 0, -4, -2, -2, 0, 0, 2, 0, -10, -10, -4, -8, -10, 4, -2, 12, 8, -10, 0, -12, 6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 27075, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '27075.f', 'trace_hash': 109657808341616065}
• 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': '0.0058834255595198134257019546898', 'prec': 97}, 'conductor': 27075, 'gens': [[2550, -1163, 1], [-420, 203272, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.68642676457511125647127487204', 'prec': 97}, {'__RealLiteral__': 0, 'data': '2.4976368999231848681128875484', 'prec': 97}], 'lmfdb_label': '27075.f1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.32754199291830234702375991848', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4922415976166975985896004581983521814', 'prec': 127}, 'tamagawa_product': 32, 'torsion_generators': [[10195, -10199, 2]], 'xcoord_integral_points': [-420, -325, 2550, 2555, 2639, 3000, 12450, 17872500]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [2, 0], '5': 'a', '7': [2, 2, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': 'a', '23': [2, 2, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '27075.f1'}
• ec_torsion_growth •

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

  
  
  • id: 1356227
    {'degree': 2, 'field': [-95, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [4]}
  • id: 1356228
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [4]}
  • id: 1356226
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 2]}
  • id: 1356230
    {'degree': 4, 'field': [49, 0, -24, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [8]}
  • id: 1356229
    {'degree': 4, 'field': [305, 40, -39, -2, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 4]}
  • id: 1356231
    {'degree': 4, 'field': [2209, 0, -96, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [8]}
  • id: 1356237
    {'degree': 8, 'field': [-64941, -77916, -48940, -4878, 465, -73, -3, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [6]}
  • id: 1356235
    {'degree': 8, 'field': [-14879, -121560, -79032, 5520, 7334, -120, -168, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [16]}
  • id: 1356232
    {'degree': 8, 'field': [495, -780, 920, -300, 201, -64, 26, -4, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 4]}
  • id: 1356233
    {'degree': 8, 'field': [1206, 1460, -94, -240, 131, -20, -14, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [8]}
  • id: 1356234
    {'degree': 8, 'field': [2609, 2668, -2080, -1132, 457, 128, -38, -4, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 8]}
  • id: 1356236
    {'degree': 8, 'field': [29761, -105480, -38712, 16560, 5894, -360, -168, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [16]}
  • id: 1356245
    {'degree': 16, 'field': [96721, 0, -545348, 0, 460048, 0, -198141, 0, 43440, 0, -6171, 0, 613, 0, -38, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [12]}
  • id: 1356238
    {'degree': 16, 'field': [236196, 0, 248560, 0, 231556, 0, 117620, 0, 35381, 0, 6380, 0, 686, 0, 40, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [4, 4]}
  • id: 1356242
    {'degree': 16, 'field': [272241, -8388360, -64248120, 54192240, 98661744, -36537480, -44980440, 5726880, 6966286, -417720, -460520, 12720, 14304, -120, -200, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 16]}
  • id: 1356240
    {'degree': 16, 'field': [648025, 0, -563400, 0, 350610, 0, -66060, 0, 24931, 0, -5436, 0, 606, 0, -36, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 8]}
  • id: 1356239
    {'degree': 16, 'field': [671695, -2436160, 1674860, 1240680, 127400, -1024520, 575260, -246000, 123721, -49848, 18928, -5656, 1610, -336, 68, -8, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 8]}
  • id: 1356243
    {'degree': 16, 'field': [19035769, 0, 3464882, 0, 200785, 0, 13329, 0, 7500, 0, 126, 0, -227, 0, -10, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [2, 6]}
  • id: 1356241
    {'degree': 16, 'field': [87314486706, -38156031720, 44502334092, -13191719832, 7868270430, -1596617208, 650771676, -106394952, 32671579, -4227560, 1027276, -102680, 20086, -1400, 220, -8, 1], 'lmfdb_label': '27075.f1', 'torsion': [16]}
  • id: 1356244
    {'degree': 16, 'field': [101153894209, 0, -34077795592, 0, 5027644960, 0, -423504009, 0, 22281240, 0, -750231, 0, 15793, 0, -190, 0, 1], 'lmfdb_label': '27075.f1', 'torsion': [12]}
• 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: 624210
    {'conductor': 27075, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '27075.f1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 624211
    {'conductor': 27075, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '27075.f1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 624212
    {'conductor': 27075, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '27075.f1', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1844567
    {'adelic_gens': [[23, 18, 6558, 7115], [3248, 2375, 7657, 1614], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [5701, 2432, 2356, 2433], [7199, 0, 0, 9119], [9089, 32, 9088, 33], [6271, 2432, 8550, 1], [343, 4826, 342, 8171]], 'adelic_image': '9120.768.13.?', 'conductor': 27075, 'lmfdb_label': '27075.f1', 'prime': 0}
  • id: 122532
    {'conductor': 27075, 'elladic_image': '16.48.0.121', 'lmfdb_label': '27075.f1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1295292
    {'lmfdb_iso': '27075.f', 'p': 11, 'prec': 20, 'unit': 54082706828863444907, 'val': 2}
  • id: 1295298
    {'lmfdb_iso': '27075.f', 'p': 13, 'prec': 20, 'unit': 58646156363582893471, 'val': 2}
  • id: 1295300
    {'lmfdb_iso': '27075.f', 'p': 17, 'prec': 20, 'unit': 48851359792982516897148, 'val': 2}
  • id: 1295297
    {'lmfdb_iso': '27075.f', 'p': 29, 'prec': 20, 'unit': 2172684520375566249386269205, 'val': 2}
  • id: 1295293
    {'lmfdb_iso': '27075.f', 'p': 37, 'prec': 20, 'unit': 98452631293712464041409843479, 'val': 2}
  • id: 1295295
    {'lmfdb_iso': '27075.f', 'p': 41, 'prec': 20, 'unit': 2072763584572081964680300738356, 'val': 2}
  • id: 1295296
    {'lmfdb_iso': '27075.f', 'p': 43, 'prec': 20, 'unit': 10192008664039468923218918043628, 'val': 2}
  • id: 1295299
    {'lmfdb_iso': '27075.f', 'p': 47, 'prec': 20, 'unit': 31630880269167894288808898747086, 'val': 2}
  • id: 1295302
    {'lmfdb_iso': '27075.f', 'p': 53, 'prec': 20, 'unit': 64066558754830042767385898789764, 'val': 2}
  • id: 1295305
    {'lmfdb_iso': '27075.f', 'p': 59, 'prec': 20, 'unit': 2114242159061530309733470738180268, 'val': 2}
  • id: 1295306
    {'lmfdb_iso': '27075.f', 'p': 61, 'prec': 20, 'unit': 6751078659923442148221337568978885, 'val': 2}
  • id: 1295301
    {'lmfdb_iso': '27075.f', 'p': 67, 'prec': 20, 'unit': 5875485408482293855802359140311999, 'val': 2}
  • id: 1295294
    {'lmfdb_iso': '27075.f', 'p': 71, 'prec': 20, 'unit': 125243230358987580858808378199866986, 'val': 2}
  • id: 1295303
    {'lmfdb_iso': '27075.f', 'p': 73, 'prec': 20, 'unit': 44479902950595234909146761993927552, 'val': 2}
  • id: 1295291
    {'lmfdb_iso': '27075.f', 'p': 83, 'prec': 20, 'unit': 1169163887426023494450254907307974455, 'val': 2}
  • id: 1295304
    {'lmfdb_iso': '27075.f', 'p': 89, 'prec': 20, 'unit': 10708989352777066586299433274548526153, 'val': 2}
  • id: 1295290
    {'lmfdb_iso': '27075.f', 'p': 97, 'prec': 20, 'unit': 50229089461210119446720622582158101511, 'val': 2}