Elliptic curve data - 30926.a4

Formats: - HTML - YAML - JSON - 2026-10-05T14:51:19.112164

• 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': '30926f', 'Clabel': '30926f2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 1056363102242, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 23688, 'ainvs': [1, 0, 1, -23241, -1364734], 'analytic_rank': 1, 'bad_primes': [2, 7, 47], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 30926, 'degree': 66240, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2395624926100040595960124528', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '30926.a', 'lmfdb_label': '30926.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': -47, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '56.12.0.k.1', '63.36.0.d.2', '72.72.1.?', '84.24.0.?', '126.108.2.?', '141.8.0.?', '168.48.1.?', '252.216.7.?', '282.24.0.?', '423.24.0.?', '504.432.21.?', '846.72.0.?', '1128.48.0.?', '2961.72.0.?', '3384.144.1.?', '3948.48.0.?', '5922.216.2.?', '7896.96.1.?', '11844.432.7.?', '23688.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9879782538792070589209640983', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 2209], [7, 8, 4418], [47, 1106, 14]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288209', 'prec': 97}, 'szpiro_ratio': 4.040345927330757, '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, 0, 2, 1, -1, 1, 0, 0, -2, 4, -1, 0, 1, 6, -1, -2, 0], 'aplist': [-1, -2, 0, 1, 0, 4, 6, -2, 0, 6, 4, 2, -6, -8, 0, 6, -6, 8, 4, 0, -2, 8, -6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 30926, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '30926.a', 'trace_hash': 549280201075664532}
• 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': '0.083816534220702644249931541560', 'prec': 97}, 'conductor': 30926, 'gens': [[4506, 58256, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '3.9879782538792070589209640983', 'prec': 97}], 'lmfdb_label': '30926.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38668553681363927901693718853', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0841870238048020241106774160929238732', 'prec': 127}, 'tamagawa_product': 8, 'torsion_generators': [[-345, 341, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [5, 0], '5': [1, 1, 0], '7': [2, 0], '11': [3, 1, 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': 'a'}, 'iwp0': 0, 'lmfdb_label': '30926.a4'}
• ec_torsion_growth •

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

  
  
  • id: 1542699
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 2]}
  • id: 1542700
    {'degree': 2, 'field': [12, -1, 1], 'lmfdb_label': '30926.a4', 'torsion': [6]}
  • id: 1542702
    {'degree': 4, 'field': [194, -20, 21, -2, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 6]}
  • id: 1542701
    {'degree': 4, 'field': [4418, 0, 47, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [4]}
  • id: 1542703
    {'degree': 6, 'field': [-55959, -1821, 3736, 59, -96, -1, 1], 'lmfdb_label': '30926.a4', 'torsion': [6]}
  • id: 1542704
    {'degree': 6, 'field': [2339, -121, 425, -21, 31, -1, 1], 'lmfdb_label': '30926.a4', 'torsion': [18]}
  • id: 1542707
    {'degree': 8, 'field': [24724, -6916, 7760, -1734, 983, -142, 52, -4, 1], 'lmfdb_label': '30926.a4', 'torsion': [12]}
  • id: 1542705
    {'degree': 8, 'field': [111556, 0, -7104, 0, -182, 0, -8, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 4]}
  • id: 1542706
    {'degree': 8, 'field': [1274641, 0, 40658, 0, 2554, 0, 50, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 4]}
  • id: 1542708
    {'degree': 12, 'field': [2099601, 0, 1558935, 0, 299782, 0, 33515, 0, 2070, 0, 71, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [3, 6]}
  • id: 1542709
    {'degree': 12, 'field': [2512657, 235438, 1325667, 50826, 284980, 3174, 32621, 0, 2088, -4, 71, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [18]}
  • id: 1542711
    {'degree': 12, 'field': [10973263, -1023918, 3190271, -247904, 408355, -28594, 31031, -1978, 1531, -84, 51, -2, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 18]}
  • id: 1542710
    {'degree': 12, 'field': [63776196, 0, 17569200, 0, 1493140, 0, 9100, 0, -2580, 0, -50, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 6]}
  • id: 1542714
    {'degree': 16, 'field': [346524304, -222759040, 292152632, -151566696, 109184622, -44250500, 22008714, -6855744, 2537545, -598008, 169986, -29344, 6468, -756, 128, -8, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 12]}
  • id: 1542713
    {'degree': 16, 'field': [1346584316, -595529088, 719652688, -264033184, 172825198, -52811488, 24245784, -6183168, 2181187, -459728, 129240, -21840, 4914, -616, 108, -8, 1], 'lmfdb_label': '30926.a4', 'torsion': [2, 12]}
  • id: 1542712
    {'degree': 16, 'field': [85740038596, 0, -9031980088, 0, 1742667958, 0, -27306604, 0, -352479, 0, -91278, 0, 6600, 0, -138, 0, 1], 'lmfdb_label': '30926.a4', 'torsion': [8]}
• 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: 720830
    {'conductor': 30926, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '30926.a4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 720831
    {'conductor': 30926, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '30926.a4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 720832
    {'conductor': 30926, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '30926.a4', 'prime': 47, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1870560
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [15652, 15651, 4089, 6346], [11087, 0, 0, 23687], [17767, 5076, 15886, 3385], [19, 36, 3240, 6139], [23653, 36, 23652, 37], [18425, 5076, 0, 1], [12409, 5076, 20586, 21433], [1, 18, 14, 253]], 'adelic_image': '23688.864.21.?', 'conductor': 30926, 'lmfdb_label': '30926.a4', 'prime': 0}
  • id: 138618
    {'conductor': 30926, 'elladic_image': '8.6.0.6', 'lmfdb_label': '30926.a4', 'modell_image': '2B', 'prime': 2}
  • id: 138619
    {'conductor': 30926, 'elladic_image': '9.12.0.1', 'lmfdb_label': '30926.a4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1498738
    {'lmfdb_iso': '30926.a', 'p': 13, 'prec': 20, 'unit': 1254887523557366334371, 'val': 1}
  • id: 1498740
    {'lmfdb_iso': '30926.a', 'p': 17, 'prec': 20, 'unit': 50485969206759737153008, 'val': 1}
  • id: 1498731
    {'lmfdb_iso': '30926.a', 'p': 19, 'prec': 20, 'unit': 1643946214151221309484727, 'val': 1}
  • id: 1498737
    {'lmfdb_iso': '30926.a', 'p': 29, 'prec': 20, 'unit': 4153299663183235335135608624, 'val': 1}
  • id: 1498747
    {'lmfdb_iso': '30926.a', 'p': 31, 'prec': 20, 'unit': 5591996017942133109502989348, 'val': 1}
  • id: 1498734
    {'lmfdb_iso': '30926.a', 'p': 37, 'prec': 20, 'unit': 169485230266920762033125154438, 'val': 1}
  • id: 1498735
    {'lmfdb_iso': '30926.a', 'p': 41, 'prec': 20, 'unit': 3140779178591287144120290303399, 'val': 1}
  • id: 1498736
    {'lmfdb_iso': '30926.a', 'p': 43, 'prec': 20, 'unit': 1736226927972565463343550226932, 'val': 1}
  • id: 1498742
    {'lmfdb_iso': '30926.a', 'p': 53, 'prec': 20, 'unit': 504540452979917602356170627755264, 'val': 1}
  • id: 1498745
    {'lmfdb_iso': '30926.a', 'p': 59, 'prec': 20, 'unit': 375887302853604519933239993046040, 'val': 1}
  • id: 1498746
    {'lmfdb_iso': '30926.a', 'p': 61, 'prec': 20, 'unit': 5627922663955930649172793274426413, 'val': 1}
  • id: 1498733
    {'lmfdb_iso': '30926.a', 'p': 67, 'prec': 20, 'unit': 357260595799249443029269212274776, 'val': 1}
  • id: 1498743
    {'lmfdb_iso': '30926.a', 'p': 73, 'prec': 20, 'unit': 103048839689691658386311156387358101, 'val': 1}
  • id: 1498739
    {'lmfdb_iso': '30926.a', 'p': 79, 'prec': 20, 'unit': 853862784653904605028773556375426805, 'val': 1}
  • id: 1498741
    {'lmfdb_iso': '30926.a', 'p': 83, 'prec': 20, 'unit': 2738870481237049706948799596130301956, 'val': 1}
  • id: 1498744
    {'lmfdb_iso': '30926.a', 'p': 89, 'prec': 20, 'unit': 121404244027642327554560785375937538, 'val': 2}
  • id: 1498732
    {'lmfdb_iso': '30926.a', 'p': 97, 'prec': 20, 'unit': 17943496290943157752122387225920602755, 'val': 1}