Elliptic curve data - 1575.j2

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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': '1575c', 'Clabel': '1575c1', 'Cnumber': 1, 'abc_quality': 0.8394167977331788, 'absD': 120558375, 'adelic_genus': 3, 'adelic_index': 96, 'adelic_level': 1680, 'ainvs': [1, -1, 0, 93, -424], 'analytic_rank': 1, 'bad_primes': [3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1575, 'degree': 384, 'elladic_images': ['8.12.0.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.23636515171559866908877000377', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [35937, 49], 'lmfdb_iso': '1575.j', 'lmfdb_label': '1575.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 10, 12], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '8.12.0.v.1', '28.12.0.n.1', '30.6.0.a.1', '48.24.0.m.1', '56.24.0.ed.1', '60.12.0.bj.1', '80.24.0.?', '120.24.0.?', '240.48.0.?', '336.48.1.?', '420.24.0.?', '560.48.1.?', '840.48.1.?', '1680.96.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7202730826931517149229941709', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 2, 175], [5, 10, 63], [7, 8, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.98995354289400869310785375723', 'prec': 107}, 'szpiro_ratio': 3.465082927342656, '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, 1, -3, 0, 0, 0, 0, -4, 1, 0, -1, 2, 0, 0, 0], 'aplist': [1, 0, 0, 1, 0, -4, 2, 0, 0, -8, -4, -8, -4, -8, -12, 6, -8, 10, -8, 16, -12, -8, 16, 12, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 1575, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1575.j', 'trace_hash': 1127052775304495530}
• 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': '0.62329814988387864297046961627', 'prec': 103}, 'conductor': 1575, 'gens': [[8, 24, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7202730826931517149229941709', 'prec': 100}], 'lmfdb_label': '1575.j2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.99163738727769693640523243831', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4117742102519729084501603222073732985', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[4, -2, 1]], 'xcoord_integral_points': [4, 8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 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': '1575.j2'}
• ec_torsion_growth •

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

  
  
  • id: 77806
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '1575.j2', 'torsion': [2, 2]}
  • id: 77807
    {'degree': 4, 'field': [1, -8, 9, -2, 1], 'lmfdb_label': '1575.j2', 'torsion': [4]}
  • id: 77810
    {'degree': 8, 'field': [-49, 49, -28, -43, 25, -7, 7, -4, 1], 'lmfdb_label': '1575.j2', 'torsion': [6]}
  • id: 77809
    {'degree': 8, 'field': [1, 0, -11, 0, 36, 0, -11, 0, 1], 'lmfdb_label': '1575.j2', 'torsion': [2, 4]}
  • id: 77808
    {'degree': 8, 'field': [46, -58, 125, -88, 94, -32, 20, -2, 1], 'lmfdb_label': '1575.j2', 'torsion': [2, 4]}
  • id: 77812
    {'degree': 16, 'field': [-1904, -672, 21568, -54880, 71020, -64368, 46864, -27420, 12769, -5300, 2026, -616, 230, -100, 22, -4, 1], 'lmfdb_label': '1575.j2', 'torsion': [8]}
  • id: 77813
    {'degree': 16, 'field': [121, -407, 1017, -1767, 2565, -3030, 3136, -2834, 2301, -1641, 1041, -576, 278, -112, 36, -8, 1], 'lmfdb_label': '1575.j2', 'torsion': [2, 6]}
  • id: 77811
    {'degree': 16, 'field': [2116, 0, -8136, 0, 14065, 0, -13884, 0, 8064, 0, -2634, 0, 460, 0, -36, 0, 1], 'lmfdb_label': '1575.j2', 'torsion': [4, 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: 24279
    {'conductor': 1575, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1575.j2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 24280
    {'conductor': 1575, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1575.j2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 24281
    {'conductor': 1575, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1575.j2', 'prime': 7, '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: 1674295
    {'adelic_gens': [[3, 28, 1604, 971], [1, 16, 0, 1], [11, 16, 1616, 1587], [1136, 5, 51, 16], [1205, 26, 1334, 1129], [13, 8, 8, 5], [1, 0, 16, 1], [1471, 16, 0, 1], [1665, 16, 1664, 17], [421, 16, 0, 1], [1016, 5, 387, 32]], 'adelic_image': '1680.96.3.?', 'conductor': 1575, 'lmfdb_label': '1575.j2', 'prime': 0}
  • id: 7524
    {'conductor': 1575, 'elladic_image': '8.12.0.31', 'lmfdb_label': '1575.j2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 41891
    {'lmfdb_iso': '1575.j', 'p': 13, 'prec': 20, 'unit': 510443097603353072481, 'val': 1}
  • id: 41893
    {'lmfdb_iso': '1575.j', 'p': 17, 'prec': 20, 'unit': 143460652583349629006990, 'val': 1}
  • id: 41890
    {'lmfdb_iso': '1575.j', 'p': 29, 'prec': 20, 'unit': 6060590784465673096100784239, 'val': 1}
  • id: 41901
    {'lmfdb_iso': '1575.j', 'p': 31, 'prec': 20, 'unit': 1319895120438503771665993504, 'val': 1}
  • id: 41886
    {'lmfdb_iso': '1575.j', 'p': 37, 'prec': 20, 'unit': 565616402793288709922278457588, 'val': 1}
  • id: 41888
    {'lmfdb_iso': '1575.j', 'p': 41, 'prec': 20, 'unit': 122303583672148282340789728715, 'val': 1}
  • id: 41889
    {'lmfdb_iso': '1575.j', 'p': 43, 'prec': 20, 'unit': 4765941729947790088082318279066, 'val': 1}
  • id: 41899
    {'lmfdb_iso': '1575.j', 'p': 47, 'prec': 20, 'unit': 54937186653680053223416156023045, 'val': 1}
  • id: 41895
    {'lmfdb_iso': '1575.j', 'p': 53, 'prec': 20, 'unit': 95893746793573368810191216686186, 'val': 1}
  • id: 41896
    {'lmfdb_iso': '1575.j', 'p': 59, 'prec': 20, 'unit': 2501761139193774817971872076059978, 'val': 1}
  • id: 41900
    {'lmfdb_iso': '1575.j', 'p': 61, 'prec': 20, 'unit': 1846065339395139351093232589038208, 'val': 1}
  • id: 41885
    {'lmfdb_iso': '1575.j', 'p': 67, 'prec': 20, 'unit': 28168021825710692797602845844881968, 'val': 1}
  • id: 41887
    {'lmfdb_iso': '1575.j', 'p': 71, 'prec': 20, 'unit': 89550890306828279729330914951206865, 'val': 1}
  • id: 41897
    {'lmfdb_iso': '1575.j', 'p': 73, 'prec': 20, 'unit': 68328565418453742793433615254918532, 'val': 1}
  • id: 41892
    {'lmfdb_iso': '1575.j', 'p': 79, 'prec': 20, 'unit': 78403174285836790283440169462733119, 'val': 1}
  • id: 41894
    {'lmfdb_iso': '1575.j', 'p': 83, 'prec': 20, 'unit': 502982335983018624940711336412232394, 'val': 1}
  • id: 41898
    {'lmfdb_iso': '1575.j', 'p': 89, 'prec': 20, 'unit': 1416981624070534376587496343301542316, 'val': 1}
  • id: 41884
    {'lmfdb_iso': '1575.j', 'p': 97, 'prec': 20, 'unit': 32280127452441931425779410087732564820, 'val': 1}