Elliptic curve data - 6930.a1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '6930g', 'Clabel': '6930g5', 'Cnumber': 5, 'abc_quality': 0.990376770318753, 'absD': 1378280445876180, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [1, -1, 0, -426105, 107150665], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6930, 'degree': 65536, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9145083734989810505854415122', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [11736717412386894481, 1890645330420], 'lmfdb_iso': '6930.a', 'lmfdb_label': '6930.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -47345, -3984325], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '10.6.0.a.1', '12.12.0-4.c.1.1', '20.12.0.g.1', '24.24.0-8.n.1.10', '40.24.0.bj.1', '56.24.0-8.n.1.4', '60.24.0-20.g.1.1', '120.48.0.?', '168.48.0.?', '176.24.0.?', '280.48.0.?', '528.48.0.?', '840.96.0.?', '880.48.0.?', '1232.48.0.?', '2640.96.0.?', '3696.96.0.?', '6160.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.36637781096749847233274605403', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3652022291649262048878188937', 'prec': 100}, 'szpiro_ratio': 5.710439344959177, '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, -1, 0, -1, -1, 0, 1, 1, 0, -2, 1, 0, 1, 6, 0, -4, -1], 'aplist': [-1, 0, -1, -1, 1, -2, 6, -4, 0, 2, -8, 6, 6, -4, -8, 2, 4, -2, -4, 0, 10, -16, -4, 6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 6930, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '6930.a', 'trace_hash': 1274130733362250329}
• 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': '0.021730972172311353233672277948', 'prec': 107}, 'conductor': 6930, 'gens': [[48, 9293, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.36637781096749847233274605403', 'prec': 103}], 'lmfdb_label': '6930.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.46517310774813058962579892033', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7268656790033342102032184047195740791', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[1523, -1523, 2]], 'xcoord_integral_points': [48, 356, 411, 653, 1193]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 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': '6930.a1'}
• ec_torsion_growth •

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

  
  
  • id: 363356
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [4]}
  • id: 363355
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [4]}
  • id: 363354
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 2]}
  • id: 363357
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 4]}
  • id: 363358
    {'degree': 4, 'field': [49, 0, -28, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [8]}
  • id: 363359
    {'degree': 4, 'field': [1225, 0, -140, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [8]}
  • id: 363363
    {'degree': 8, 'field': [-62208, 0, -11124, 0, -864, 0, 0, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [6]}
  • id: 363362
    {'degree': 8, 'field': [-671, 3420, -2504, -1772, 737, 176, -54, -4, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 8]}
  • id: 363361
    {'degree': 8, 'field': [1, 2, 0, 12, 19, -12, 0, -2, 1], 'lmfdb_label': '6930.a1', 'torsion': [8]}
  • id: 363360
    {'degree': 8, 'field': [960400, 0, 0, 0, 980, 0, 0, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 4]}
  • id: 363365
    {'degree': 16, 'field': [1, 2, 2, 24, 13, -74, 114, -58, -12, 44, -24, -2, 13, -12, 8, -4, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 8]}
  • id: 363370
    {'degree': 16, 'field': [1440000, 0, 797625, 0, -201350, 0, -197625, 0, 48075, 0, -2485, 0, 375, 0, -30, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [12]}
  • id: 363369
    {'degree': 16, 'field': [7767369, 0, -1578384, 0, 206140, 0, -215448, 0, 10590, 0, -3488, 0, 60, 0, -24, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [12]}
  • id: 363368
    {'degree': 16, 'field': [91202500, 0, -175277125, 0, 68865850, 0, -1832875, 0, 277675, 0, 15905, 0, -125, 0, -10, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [2, 6]}
  • id: 363364
    {'degree': 16, 'field': [3573767961, 0, 173353188, 0, -20640242, 0, -3107524, 0, 188475, 0, 1036, 0, -462, 0, 8, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [4, 4]}
  • id: 363366
    {'degree': 16, 'field': [3471607400625, 0, -2432179386000, 0, 409447332000, 0, -29376632880, 0, 1041091191, 0, -18691344, 0, 164640, 0, -672, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [16]}
  • id: 363367
    {'degree': 16, 'field': [933091085928960000, 0, -17721233187840000, 0, 195155200800000, 0, -1729880712000, 0, 14408892225, 0, -86259600, 0, 338100, 0, -840, 0, 1], 'lmfdb_label': '6930.a1', 'torsion': [16]}
• 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: 141222
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6930.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 141223
    {'conductor': 6930, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '6930.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 141224
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6930.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 141225
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6930.a1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 141226
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6930.a1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 1709703
    {'adelic_gens': [[5, 4, 18476, 18477], [13, 16, 13604, 13545], [16183, 16, 11814, 14185], [1, 16, 0, 1], [12307, 18464, 6416, 315], [18465, 16, 18464, 17], [11096, 1, 14863, 10], [1, 0, 16, 1], [15, 2, 18382, 18467], [13213, 16, 15584, 18165], [11761, 16, 1688, 129]], 'adelic_image': '18480.192.1.?', 'conductor': 6930, 'lmfdb_label': '6930.a1', 'prime': 0}
  • id: 34130
    {'conductor': 6930, 'elladic_image': '8.12.0.5', 'lmfdb_label': '6930.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 278705
    {'lmfdb_iso': '6930.a', 'p': 13, 'prec': 20, 'unit': 985847207807025011158, 'val': 1}
  • id: 278707
    {'lmfdb_iso': '6930.a', 'p': 17, 'prec': 20, 'unit': 130249641715020440839207, 'val': 1}
  • id: 278708
    {'lmfdb_iso': '6930.a', 'p': 19, 'prec': 20, 'unit': 1526877687974673821502020, 'val': 1}
  • id: 278704
    {'lmfdb_iso': '6930.a', 'p': 29, 'prec': 20, 'unit': 2510505604051325226352950127, 'val': 1}
  • id: 278715
    {'lmfdb_iso': '6930.a', 'p': 31, 'prec': 20, 'unit': 11282842742903755991189873595, 'val': 1}
  • id: 278701
    {'lmfdb_iso': '6930.a', 'p': 37, 'prec': 20, 'unit': 203265917554620840728473579797, 'val': 1}
  • id: 278702
    {'lmfdb_iso': '6930.a', 'p': 41, 'prec': 20, 'unit': 3890704523134514832982569107, 'val': 1}
  • id: 278703
    {'lmfdb_iso': '6930.a', 'p': 43, 'prec': 20, 'unit': 8089870245620267313373507481309, 'val': 1}
  • id: 278713
    {'lmfdb_iso': '6930.a', 'p': 47, 'prec': 20, 'unit': 7425474878689512589436815110220, 'val': 1}
  • id: 278709
    {'lmfdb_iso': '6930.a', 'p': 53, 'prec': 20, 'unit': 301571904733665918946561401237131, 'val': 1}
  • id: 278710
    {'lmfdb_iso': '6930.a', 'p': 59, 'prec': 20, 'unit': 2914826314348189019945715731090285, 'val': 1}
  • id: 278714
    {'lmfdb_iso': '6930.a', 'p': 61, 'prec': 20, 'unit': 4708793656096520322434927646519570, 'val': 1}
  • id: 278700
    {'lmfdb_iso': '6930.a', 'p': 67, 'prec': 20, 'unit': 10504611520215234868253226339003079, 'val': 1}
  • id: 278711
    {'lmfdb_iso': '6930.a', 'p': 73, 'prec': 20, 'unit': 57895915294430950162526489705212516, 'val': 1}
  • id: 278706
    {'lmfdb_iso': '6930.a', 'p': 79, 'prec': 20, 'unit': 54473965631923661480129092636151509, 'val': 1}
  • id: 278699
    {'lmfdb_iso': '6930.a', 'p': 83, 'prec': 20, 'unit': 337180920700293811252167320572366288, 'val': 1}
  • id: 278712
    {'lmfdb_iso': '6930.a', 'p': 89, 'prec': 20, 'unit': 9744144982202579187776830508022684720, 'val': 1}
  • id: 278698
    {'lmfdb_iso': '6930.a', 'p': 97, 'prec': 20, 'unit': 25544866231792343754243358416757828505, 'val': 1}