Elliptic curve data - 30.a4

Formats: - HTML - YAML - JSON - 2026-07-19T00:36:54.268027

• 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': '30a', 'Clabel': '30a5', 'Cnumber': 5, 'abc_quality': 1.0501740895315954, 'absD': 33750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -289, 1862], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 8, 'elladic_images': ['8.12.0.8', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'faltings_index': 4, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2656166199049, 33750], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 1862], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.4', '12.96.0-12.c.4.5', '24.192.1-24.da.3.4', '40.24.0-40.bb.1.14', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 3], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'szpiro_ratio': 8.411127526667551, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 1, 1, -1, -1, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1], 'aplist': [-1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2, -6, -4, 0, -6, 0, -10, -4, 0, 2, 8, 12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 30, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '30.a', 'trace_hash': 148452494971348580}
• 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': '0.97071760525957984774787504161', 'prec': 103}, 'conductor': 30, 'gens': [], 'heights': [], 'lmfdb_label': '30.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.3519482592414964494482281339', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.55865804320691607490803802232401598477', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [[16, 29, 1]], 'xcoord_integral_points': [10, 16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [1, 0], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '30.a4'}
• ec_torsion_growth •

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

  
  
  • id: 739
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 6]}
  • id: 741
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [12]}
  • id: 740
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [12]}
  • id: 742
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 12]}
  • id: 743
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '30.a4', 'torsion': [3, 6]}
  • id: 746
    {'degree': 8, 'field': [4, 12, 14, 0, 6, -6, 5, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [24]}
  • id: 745
    {'degree': 8, 'field': [36, 0, -144, 0, 82, 0, -16, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [24]}
  • id: 744
    {'degree': 8, 'field': [36, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 12]}
  • id: 747
    {'degree': 9, 'field': [16, -48, 0, 44, -24, -24, 11, 0, -3, 1], 'lmfdb_label': '30.a4', 'torsion': [18]}
  • id: 748
    {'degree': 12, 'field': [4, 0, -24, 0, 156, 0, 76, 0, 24, 0, 6, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [6, 6]}
  • id: 749
    {'degree': 12, 'field': [4, 0, 24, 0, 156, 0, -76, 0, 24, 0, -6, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [3, 12]}
  • id: 750
    {'degree': 12, 'field': [9, 0, 21, 0, 46, 0, 1, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [3, 12]}
  • id: 752
    {'degree': 16, 'field': [1, 0, -20, 0, 128, 0, -360, 0, 503, 0, -360, 0, 128, 0, -20, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 24]}
  • id: 753
    {'degree': 16, 'field': [16, 0, 48, 0, 52, 0, 48, 0, 168, 0, 24, 0, 13, 0, 6, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 24]}
  • id: 751
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [4, 12]}
  • id: 754
    {'degree': 18, 'field': [-69984, 0, 804816, 0, -11664, 0, -134460, 0, 648, 0, 9612, 0, -618, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [2, 18]}
  • id: 756
    {'degree': 18, 'field': [-6912, 0, 41472, 0, -31104, 0, 3888, 0, 7344, 0, -1944, 0, -531, 0, 234, 0, -27, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [36]}
  • id: 755
    {'degree': 18, 'field': [-2592, 0, 42768, 0, 1296, 0, 9684, 0, 0, 0, 576, 0, -422, 0, 48, 0, -6, 0, 1], 'lmfdb_label': '30.a4', 'torsion': [36]}
• 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: 96
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '30.a4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 97
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '30.a4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 98
    {'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '30.a4', 'prime': 5, 'reduction_type': -1, '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: 1665936
    {'adelic_gens': [[1, 12, 12, 25], [1, 24, 0, 1], [97, 24, 96, 25], [1, 0, 24, 1], [16, 81, 95, 26], [6, 49, 35, 56], [15, 106, 14, 11], [94, 3, 15, 34], [97, 24, 84, 49]], 'adelic_image': '120.384.5.?', 'conductor': 30, 'lmfdb_label': '30.a4', 'prime': 0}
  • id: 61
    {'conductor': 30, 'elladic_image': '8.12.0.8', 'lmfdb_label': '30.a4', 'modell_image': '2B', 'prime': 2}
  • id: 62
    {'conductor': 30, 'elladic_image': '3.8.0.1', 'lmfdb_label': '30.a4', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 30.a does not appear in ec_padic