Elliptic curve data - 7938.x3

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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': '7938u', 'Clabel': '7938u1', 'Cnumber': 1, 'abc_quality': 1.1780968639246816, 'absD': 76236552, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [1, -1, 1, -230, -1347], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 7938, 'degree': 2160, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.16.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.26936807887764018183084025072', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-140625, 8], 'lmfdb_iso': '7938.x', 'lmfdb_label': '7938.x3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -42, -100], 'min_quad_twist_disc': 21, 'modell_images': ['3B', '7B.2.3'], 'modm_images': ['3.4.0.a.1', '7.16.0-7.a.1.1', '8.2.0.a.1', '21.128.1-21.a.3.4', '24.8.0.a.1', '56.32.0-56.a.1.2', '63.384.5-63.e.4.4', '168.256.5.?', '504.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6793060523796833019195517156', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3969], [3, 8, 49], [7, 26, 162]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0697910918727197011869178666', 'prec': 103}, 'szpiro_ratio': 3.120194820753294, '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, 1, 0, 1, 0, 0, 0, 1, 0, 0, -3, 0, -2, 0, 0, 1, 3, 0, 1, 0], 'aplist': [1, 0, 0, 0, -3, -2, 3, 1, -6, 6, 4, -4, -9, -1, 6, 12, -3, -8, 5, -12, -11, -4, -12, -6, -5], 'class_deg': 21, 'class_size': 4, 'conductor': 7938, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '7938.x', 'trace_hash': 676935966248814078}
• 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': '0.58348521984058875136882165160', 'prec': 103}, 'conductor': 7938, 'gens': [[51, 317, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6793060523796833019195517156', 'prec': 100}], 'lmfdb_label': '7938.x3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.61115798821087196476372740805', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1579278513762505534996350877009544295', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [51]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': 'a', '5': [1, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7938.x3'}
• ec_torsion_growth •

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

  
  
  • id: 415332
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '7938.x3', 'torsion': [3]}
  • id: 415333
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [2]}
  • id: 415335
    {'degree': 6, 'field': [-3, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [3]}
  • id: 415336
    {'degree': 6, 'field': [8, -12, 36, -5, 9, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [21]}
  • id: 415334
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [2, 2]}
  • id: 415337
    {'degree': 6, 'field': [224, -168, -12, 19, 3, -3, 1], 'lmfdb_label': '7938.x3', 'torsion': [6]}
  • id: 415339
    {'degree': 12, 'field': [576, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [3, 3]}
  • id: 415340
    {'degree': 12, 'field': [1808, -3216, 3036, 256, 168, -456, 321, -150, 51, -20, 15, -6, 1], 'lmfdb_label': '7938.x3', 'torsion': [2, 6]}
  • id: 415338
    {'degree': 12, 'field': [40328, 176928, -63276, -6248, 38190, -19224, 7725, -1362, 363, -68, 33, -6, 1], 'lmfdb_label': '7938.x3', 'torsion': [4]}
  • id: 415342
    {'degree': 18, 'field': [-380880, -789912, -507924, -68688, 172044, 94122, 25011, -2754, -9261, -5718, 540, 306, 243, 54, 0, -6, -9, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [6]}
  • id: 415343
    {'degree': 18, 'field': [512, 0, 2304, 960, 4896, 1680, 5256, 576, 3174, -403, 1332, -444, 473, -189, 123, -35, 18, -3, 1], 'lmfdb_label': '7938.x3', 'torsion': [42]}
  • id: 415341
    {'degree': 18, 'field': [83024, -106416, 163224, -98868, 70056, -51912, 47076, -30078, 16794, -8627, 4851, -2718, 1350, -504, 180, -84, 36, -9, 1], 'lmfdb_label': '7938.x3', 'torsion': [9]}
  • id: 415344
    {'degree': 21, 'field': [11494, 28266, -9702, -75620, -48594, 40320, 52888, -9723, -24948, 1395, 7770, -2457, -1072, 1869, 126, -843, 0, 189, -2, -21, 0, 1], 'lmfdb_label': '7938.x3', 'torsion': [7]}
• 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: 164295
    {'conductor': 7938, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '7938.x3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 164296
    {'conductor': 7938, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '7938.x3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 164297
    {'conductor': 7938, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7938.x3', 'prime': 7, 'reduction_type': 0, '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: 1716415
    {'adelic_gens': [[281, 392, 112, 393], [1, 426, 42, 253], [1, 216, 0, 1], [1, 0, 462, 1], [85, 42, 189, 43], [337, 168, 336, 169], [1, 0, 168, 1], [295, 42, 231, 211], [22, 321, 189, 169], [1, 0, 420, 1], [1, 168, 0, 1], [177, 10, 448, 417], [503, 462, 0, 431], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 7938, 'lmfdb_label': '7938.x3', 'prime': 0}
  • id: 38893
    {'conductor': 7938, 'elladic_image': '8.2.0.1', 'lmfdb_label': '7938.x3', 'modell_image': '2G', 'prime': 2}
  • id: 38894
    {'conductor': 7938, 'elladic_image': '3.4.0.1', 'lmfdb_label': '7938.x3', 'modell_image': '3B', 'prime': 3}
  • id: 38895
    {'conductor': 7938, 'elladic_image': '7.16.0.2', 'lmfdb_label': '7938.x3', 'modell_image': '7B.2.3', 'prime': 7}
• ec_padic •

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

  
  
  • id: 326023
    {'lmfdb_iso': '7938.x', 'p': 11, 'prec': 20, 'unit': 26495890738773756748, 'val': 1}
  • id: 326029
    {'lmfdb_iso': '7938.x', 'p': 13, 'prec': 20, 'unit': 78594010624001306244, 'val': 1}
  • id: 326031
    {'lmfdb_iso': '7938.x', 'p': 17, 'prec': 20, 'unit': 93426255524138851996913, 'val': 1}
  • id: 326032
    {'lmfdb_iso': '7938.x', 'p': 19, 'prec': 20, 'unit': 5571479067794481528392658, 'val': -1}
  • id: 326036
    {'lmfdb_iso': '7938.x', 'p': 23, 'prec': 20, 'unit': 50982914448000551301976154, 'val': 1}
  • id: 326028
    {'lmfdb_iso': '7938.x', 'p': 29, 'prec': 20, 'unit': 2076252466304371189194401004, 'val': 1}
  • id: 326041
    {'lmfdb_iso': '7938.x', 'p': 31, 'prec': 20, 'unit': 17008460411327068922543960956, 'val': 1}
  • id: 326024
    {'lmfdb_iso': '7938.x', 'p': 37, 'prec': 20, 'unit': 12025994010729928223664499106, 'val': 1}
  • id: 326026
    {'lmfdb_iso': '7938.x', 'p': 41, 'prec': 20, 'unit': 901082234027974466643973219952, 'val': 1}
  • id: 326027
    {'lmfdb_iso': '7938.x', 'p': 43, 'prec': 20, 'unit': 2167315866490244977555300374890, 'val': 1}
  • id: 326038
    {'lmfdb_iso': '7938.x', 'p': 47, 'prec': 20, 'unit': 44461716475381546583777821075474, 'val': 1}
  • id: 326033
    {'lmfdb_iso': '7938.x', 'p': 53, 'prec': 20, 'unit': 335666715708882980957700938007587, 'val': 1}
  • id: 326034
    {'lmfdb_iso': '7938.x', 'p': 59, 'prec': 20, 'unit': 2243876074067014366887082093085723, 'val': 1}
  • id: 326039
    {'lmfdb_iso': '7938.x', 'p': 61, 'prec': 20, 'unit': 2376968438604158123023028749675452, 'val': 1}
  • id: 326022
    {'lmfdb_iso': '7938.x', 'p': 67, 'prec': 20, 'unit': 15210320049904805571068802215765341, 'val': 1}
  • id: 326025
    {'lmfdb_iso': '7938.x', 'p': 71, 'prec': 20, 'unit': 139024692232912998071995531148383093, 'val': 1}
  • id: 326035
    {'lmfdb_iso': '7938.x', 'p': 73, 'prec': 20, 'unit': 213545717624148386545845171510102945, 'val': 1}
  • id: 326030
    {'lmfdb_iso': '7938.x', 'p': 79, 'prec': 20, 'unit': 686730913596404318955141814695393340, 'val': 1}
  • id: 326040
    {'lmfdb_iso': '7938.x', 'p': 83, 'prec': 20, 'unit': 10998844869429977019351540546719989, 'val': 2}
  • id: 326037
    {'lmfdb_iso': '7938.x', 'p': 89, 'prec': 20, 'unit': 2096066966895897197720677125242335851, 'val': 1}
  • id: 326021
    {'lmfdb_iso': '7938.x', 'p': 97, 'prec': 20, 'unit': 22809655259234730773830834956560174235, 'val': 1}