Elliptic curve data - 15730.s2

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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': '15730y', 'Clabel': '15730y1', 'Cnumber': 1, 'abc_quality': 0.906187683689355, 'absD': 46060586000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 17160, 'ainvs': [1, 0, 0, -3935, -94775], 'analytic_rank': 0, 'bad_primes': [2, 5, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 15730, 'degree': 25920, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.88009089454279401192318561520', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [3803721481, 26000], 'lmfdb_iso': '15730.s', 'lmfdb_label': '15730.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -33, 68], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.br.1', '33.8.0-3.a.1.2', '66.24.0-6.a.1.2', '88.12.0.?', '130.6.0.?', '132.48.0.?', '260.24.0.?', '264.96.0.?', '390.24.0.?', '780.96.3.?', '1560.192.9.?', '4290.48.0.?', '5720.48.0.?', '8580.192.3.?', '17160.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 7865], [3, 2, 3146], [5, 6, 3146], [11, 62, 130], [13, 14, 1210]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31885674185639126010778617378', 'prec': 107}, 'szpiro_ratio': 3.77164355056109, '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, -2, 1, 1, -2, 4, 1, 1, 1, 0, -2, -1, 4, -2, 1, 6, 1, -2, 1], 'aplist': [1, -2, 1, 4, 0, -1, 6, -2, 6, 6, 2, 2, 6, -2, -12, 6, 6, -2, -4, -6, 10, 4, 0, -6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 15730, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '15730.s', 'trace_hash': 837590040550465396}
• 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': '0.17201359078721043849070287893', 'prec': 103}, 'conductor': 15730, 'gens': [], 'heights': [], 'lmfdb_label': '15730.s2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60303384343642740867015188953', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6182030606185644520209113371755342974', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-34, 17, 1]], 'xcoord_integral_points': [-34]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [4, 0], '5': [3, 0], '11': 'a', '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '15730.s2'}
• ec_torsion_growth •

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

  
  
  • id: 808112
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 2]}
  • id: 808113
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '15730.s2', 'torsion': [6]}
  • id: 808115
    {'degree': 4, 'field': [361, 0, -27, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 6]}
  • id: 808114
    {'degree': 4, 'field': [482, 38, -37, -2, 1], 'lmfdb_label': '15730.s2', 'torsion': [4]}
  • id: 808116
    {'degree': 6, 'field': [-216, -36, -122, -75, 1, -3, 1], 'lmfdb_label': '15730.s2', 'torsion': [6]}
  • id: 808119
    {'degree': 8, 'field': [4, 0, 8, 0, 85, 0, -18, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [12]}
  • id: 808117
    {'degree': 8, 'field': [13456, 0, 4345, 0, 703, 0, 55, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 4]}
  • id: 808118
    {'degree': 8, 'field': [20736, 0, -9081, 0, 1151, 0, -71, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 4]}
  • id: 808121
    {'degree': 12, 'field': [-98996, 1604396, -640612, 92188, 17274, 6064, -13637, 2174, -1395, -196, 5, -2, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 6]}
  • id: 808120
    {'degree': 12, 'field': [324, -2268, 5112, 1260, 1360, 276, 455, -357, 6, 21, -4, -3, 1], 'lmfdb_label': '15730.s2', 'torsion': [3, 6]}
  • id: 808123
    {'degree': 16, 'field': [35060, 66640, 8920, -8240, 16521, -12712, 6872, -11316, 6700, -4332, 2138, -848, 400, -84, 32, -4, 1], 'lmfdb_label': '15730.s2', 'torsion': [24]}
  • id: 808124
    {'degree': 16, 'field': [112225, 0, -205680, 0, 189646, 0, -97048, 0, 29959, 0, -6104, 0, 814, 0, -48, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 12]}
  • id: 808125
    {'degree': 16, 'field': [2072240, -1696060, 2843985, -2046170, 1548106, -953436, 471165, -226200, 89351, -27900, 7149, -800, -309, 120, 0, -6, 1], 'lmfdb_label': '15730.s2', 'torsion': [2, 12]}
  • id: 808122
    {'degree': 16, 'field': [71233600, 0, 108522400, 0, 49531380, 0, 11641480, 0, 1696641, 0, 143944, 0, 6986, 0, 144, 0, 1], 'lmfdb_label': '15730.s2', 'torsion': [4, 4]}
  • id: 808126
    {'degree': 18, 'field': [2763875, -7335900, 10407060, -10630513, 8322447, -5193636, 2737208, -1272639, 551472, -219231, 78993, -20259, 3337, 465, -111, 38, 21, -3, 1], 'lmfdb_label': '15730.s2', 'torsion': [18]}
• 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: 348580
    {'conductor': 15730, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '15730.s2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 348581
    {'conductor': 15730, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '15730.s2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 348582
    {'conductor': 15730, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15730.s2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 348583
    {'conductor': 15730, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15730.s2', 'prime': 13, '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: 1768794
    {'adelic_gens': [[1, 12, 12, 145], [9359, 0, 0, 17159], [5721, 3124, 4180, 11001], [7, 24, 492, 1687], [1266, 14047, 209, 10880], [17137, 24, 17136, 25], [1, 24, 0, 1], [11056, 7821, 11715, 7426], [21, 4, 17060, 17141], [1, 0, 24, 1], [8581, 1584, 8580, 1], [12871, 1584, 0, 1]], 'adelic_image': '17160.384.9.?', 'conductor': 15730, 'lmfdb_label': '15730.s2', 'prime': 0}
  • id: 74130
    {'conductor': 15730, 'elladic_image': '4.6.0.3', 'lmfdb_label': '15730.s2', 'modell_image': '2B', 'prime': 2}
  • id: 74131
    {'conductor': 15730, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15730.s2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15730.s does not appear in ec_padic