Elliptic curve data - 13475.v1

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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': '13475j', 'Clabel': '13475j3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 20220921875, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 3850, 'ainvs': [0, -1, 1, -9579908, 11415939093], 'analytic_rank': 1, 'bad_primes': [5, 7, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 13475, 'degree': 252000, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2743831458433539624644214435', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '13475.v', 'lmfdb_label': '13475.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': -35, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '22.2.0.a.1', '25.60.0.a.2', '35.24.0-5.a.2.1', '110.24.1.?', '175.120.0.?', '275.300.12.?', '550.600.37.?', '770.48.1.?', '1925.600.12.?', '3850.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.7537795364446427876805605330', 'prec': 100}, 'semistable': False, 'serre_invariants': [[5, 14, 539], [7, 26, 275], [11, 12, 1225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540517', 'prec': 103}, 'szpiro_ratio': 6.293165442293153, '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, 2, -1, 2, 0, -2, 0, 0, -2, 0, 1, -2, 4, 0, 0, -4, -2, -4, 0, 0], 'aplist': [2, -1, 0, 0, 1, 4, -2, 0, 1, 0, -7, -3, 8, 6, 8, 6, -5, -12, 7, -3, 4, -10, -6, -15, -7], 'class_deg': 25, 'class_size': 3, 'conductor': 13475, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '13475.v', 'trace_hash': 1719119918666817800}
• 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': '0.010580249276891196101188609782', 'prec': 107}, 'conductor': 13475, 'gens': [[10874029, -198125, 78]], 'heights': [{'__RealLiteral__': 0, 'data': '7.7537795364446427876805605330', 'prec': 100}], 'lmfdb_label': '13475.v1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.49317002826969191536555975128', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6478633463707263171129156337780196873', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 5, 0], '3': [1, 0], '5': 'a', '7': 'a', '11': [4, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '13475.v1'}
• ec_torsion_growth •

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

  
  
  • id: 694307
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '13475.v1', 'torsion': [2]}
  • id: 694308
    {'degree': 4, 'field': [11, 9, -9, -1, 1], 'lmfdb_label': '13475.v1', 'torsion': [5]}
  • id: 694309
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '13475.v1', 'torsion': [2, 2]}
  • id: 694310
    {'degree': 8, 'field': [-34019, -20576, -9533, 1623, -537, 84, -2, -2, 1], 'lmfdb_label': '13475.v1', 'torsion': [3]}
  • id: 694311
    {'degree': 10, 'field': [55199, -25820, 42955, -17260, 9710, -2589, 1085, -190, 55, -5, 1], 'lmfdb_label': '13475.v1', 'torsion': [5]}
  • id: 694312
    {'degree': 12, 'field': [-75314594, 12008664, 8472820, 2867836, 1638532, 123364, 45116, 7932, -1702, 66, 6, -2, 1], 'lmfdb_label': '13475.v1', 'torsion': [4]}
  • id: 694313
    {'degree': 12, 'field': [2321, -10032, -7868, 3113, 4009, -896, -1317, 78, 265, 13, -25, -1, 1], 'lmfdb_label': '13475.v1', 'torsion': [10]}
  • id: 694314
    {'degree': 20, 'field': [21517195051, -174870664265, -373712335590, -47943036735, 234282460390, 67165539948, -61917017090, -18111848990, 9055215240, 2245529115, -796174676, -149800505, 42910045, 5595605, -1395645, -114998, 26105, 1205, -255, -5, 1], 'lmfdb_label': '13475.v1', 'torsion': [25]}
• 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: 294216
    {'conductor': 13475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '13475.v1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 294217
    {'conductor': 13475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '13475.v1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 294218
    {'conductor': 13475, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '13475.v1', '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: 1753570
    {'adelic_gens': [[38, 41, 1291, 1089], [1, 0, 50, 1], [3801, 50, 3800, 51], [1, 50, 0, 1], [1649, 0, 0, 3849], [1436, 2345, 3815, 2416], [1210, 2191, 973, 1987]], 'adelic_image': '3850.1200.37.?', 'conductor': 13475, 'lmfdb_label': '13475.v1', 'prime': 0}
  • id: 63966
    {'conductor': 13475, 'elladic_image': '25.60.0.2', 'lmfdb_label': '13475.v1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 595884
    {'lmfdb_iso': '13475.v', 'p': 13, 'prec': 20, 'unit': 845407758792805254522, 'val': 1}
  • id: 595886
    {'lmfdb_iso': '13475.v', 'p': 17, 'prec': 20, 'unit': 134943376694488708637720, 'val': 1}
  • id: 595891
    {'lmfdb_iso': '13475.v', 'p': 23, 'prec': 20, 'unit': 423366346095417363672875065, 'val': -1}
  • id: 595895
    {'lmfdb_iso': '13475.v', 'p': 31, 'prec': 20, 'unit': 271890200483339379610171882, 'val': 2}
  • id: 595880
    {'lmfdb_iso': '13475.v', 'p': 37, 'prec': 20, 'unit': 394511743385807094135142223554, 'val': 1}
  • id: 595882
    {'lmfdb_iso': '13475.v', 'p': 41, 'prec': 20, 'unit': 2917930092831294389603788229398, 'val': 1}
  • id: 595883
    {'lmfdb_iso': '13475.v', 'p': 43, 'prec': 20, 'unit': 9482063382723928291729500899616, 'val': 1}
  • id: 595893
    {'lmfdb_iso': '13475.v', 'p': 47, 'prec': 20, 'unit': 15608834785485783739818359850934, 'val': 1}
  • id: 595888
    {'lmfdb_iso': '13475.v', 'p': 53, 'prec': 20, 'unit': 448131664510123746606099261161273, 'val': 1}
  • id: 595889
    {'lmfdb_iso': '13475.v', 'p': 59, 'prec': 20, 'unit': 3168782171500504759223431283692720, 'val': 1}
  • id: 595894
    {'lmfdb_iso': '13475.v', 'p': 61, 'prec': 20, 'unit': 2851009598005502810401109718396492, 'val': 1}
  • id: 595879
    {'lmfdb_iso': '13475.v', 'p': 67, 'prec': 20, 'unit': 5356187551915988637128949600489297, 'val': 1}
  • id: 595881
    {'lmfdb_iso': '13475.v', 'p': 71, 'prec': 20, 'unit': 83069768112168405675009694697781934, 'val': 1}
  • id: 595890
    {'lmfdb_iso': '13475.v', 'p': 73, 'prec': 20, 'unit': 63817606578481835256182936187744688, 'val': 1}
  • id: 595885
    {'lmfdb_iso': '13475.v', 'p': 79, 'prec': 20, 'unit': 559018980052434862842129650444222817, 'val': 1}
  • id: 595887
    {'lmfdb_iso': '13475.v', 'p': 83, 'prec': 20, 'unit': 581228526567310722116766881436919398, 'val': 1}
  • id: 595892
    {'lmfdb_iso': '13475.v', 'p': 89, 'prec': 20, 'unit': 3044659118606155068331234092891399482, 'val': 1}
  • id: 595878
    {'lmfdb_iso': '13475.v', 'p': 97, 'prec': 20, 'unit': 3306885922707285705489832436063216269, 'val': 1}