Elliptic curve data - 210.d2

Formats: - HTML - YAML - JSON - 2025-10-10T20:40:06.777029

• 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': '210a', 'Clabel': '210a4', 'Cnumber': 4, 'abc_quality': 1.0250305664622372, 'absD': 2593080, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [1, 0, 0, -5761, 167825], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 210, 'degree': 192, 'elladic_images': ['8.12.0.8', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64971986870186991312831998223', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [21145699168383889, 2593080], 'lmfdb_iso': '210.d', 'lmfdb_label': '210.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5761, 167825], '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', '12.48.0-12.g.1.12', '24.96.0-24.bu.3.28', '56.24.0-56.bb.1.14', '60.96.0-60.c.3.16', '120.192.1.?', '168.192.1.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 15], [3, 4, 35], [5, 6, 42], [7, 8, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64971986870186991312831998223', 'prec': 103}, 'szpiro_ratio': 7.030008787885432, '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, 1, 1, 1, -1, 0, 1, 2, 1, -1, 1, -6, 1, -4, -1], 'aplist': [1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2, 6, 8, -12, 6, -12, 2, 8, 0, 14, -16, 12, 6, 14], 'class_deg': 12, 'class_size': 8, 'conductor': 210, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '210.d', 'trace_hash': 850949398862613817}
• 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': '0.27268452518500185779761107129', 'prec': 103}, 'conductor': 210, 'gens': [], 'heights': [], 'lmfdb_label': '210.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.9904248603555489387982512663', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9904248603555489387982512662981887046', 'prec': 130}, 'tamagawa_product': 36, 'torsion_generators': [[56, 119, 1]], 'xcoord_integral_points': [44, 56]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [0, 0], '7': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '210.d2'}
• ec_torsion_growth •

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

  
  
  • id: 8594
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 6]}
  • id: 8595
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [12]}
  • id: 8596
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [12]}
  • id: 8597
    {'degree': 4, 'field': [49, 0, -16, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 12]}
  • id: 8598
    {'degree': 6, 'field': [48, 0, -23, 0, 1, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [3, 6]}
  • id: 8600
    {'degree': 8, 'field': [196, 28, -902, 76, 550, 46, -47, -2, 1], 'lmfdb_label': '210.d2', 'torsion': [24]}
  • id: 8601
    {'degree': 8, 'field': [3600, 0, 1920, 0, 166, 0, -24, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [24]}
  • id: 8599
    {'degree': 8, 'field': [14400, 0, 0, 0, 210, 0, 0, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 12]}
  • id: 8602
    {'degree': 9, 'field': [256, -192, -1872, 2876, -1032, 12, 71, -9, -3, 1], 'lmfdb_label': '210.d2', 'torsion': [18]}
  • id: 8604
    {'degree': 12, 'field': [3969, 0, 75852, 0, 13720, 0, 3590, 0, 360, 0, 32, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [3, 12]}
  • id: 8605
    {'degree': 12, 'field': [7804, -15912, 8138, 2748, -3411, 1314, -617, 42, 126, -54, 23, -6, 1], 'lmfdb_label': '210.d2', 'torsion': [3, 12]}
  • id: 8603
    {'degree': 12, 'field': [386884, 0, 879212, 0, 178365, 0, 22330, 0, 1515, 0, 62, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [6, 6]}
  • id: 8608
    {'degree': 16, 'field': [38416, 0, -10976, 0, 29792, 0, 2520, 0, 7121, 0, -180, 0, 152, 0, 4, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 24]}
  • id: 8607
    {'degree': 16, 'field': [112896, 0, -596736, 0, 701520, 0, -359184, 0, 96964, 0, -14744, 0, 1260, 0, -56, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 24]}
  • id: 8606
    {'degree': 16, 'field': [12960000, 0, -12960000, 0, 6480000, 0, -1890000, 0, 335025, 0, -31500, 0, 1800, 0, -60, 0, 1], 'lmfdb_label': '210.d2', 'torsion': [4, 12]}
  • id: 8609
    {'degree': 18, 'field': [-20348132924, 15282699096, 2240157780, -6603714920, 1824100356, 758370048, -394224172, -3279744, 20107824, -1504556, 108240, -97020, 1739, 3066, -861, 196, -9, -6, 1], 'lmfdb_label': '210.d2', 'torsion': [2, 18]}
  • id: 8610
    {'degree': 18, 'field': [-8994636, -91668024, 175558320, -134886384, 30617244, -16014348, 840876, 3205476, 502182, 52572, 90756, 59868, -9587, -384, -1839, 310, -3, -6, 1], 'lmfdb_label': '210.d2', 'torsion': [36]}
  • id: 8611
    {'degree': 18, 'field': [-93312, 0, -404352, 0, -508896, 0, -158144, 0, -47352, 0, 71880, 0, -16618, 0, 1572, 0, -66, 0, 1], 'lmfdb_label': '210.d2', '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: 1760
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '210.d2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1761
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '210.d2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1762
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '210.d2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1763
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '210.d2', 'prime': 7, 'reduction_type': 1, '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: 1666661
    {'adelic_gens': [[15, 106, 374, 11], [16, 441, 695, 746], [352, 21, 555, 466], [1, 12, 12, 145], [246, 409, 35, 176], [817, 24, 816, 25], [1, 24, 0, 1], [214, 3, 255, 34], [241, 24, 372, 289], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 210, 'lmfdb_label': '210.d2', 'prime': 0}
  • id: 887
    {'conductor': 210, 'elladic_image': '8.12.0.8', 'lmfdb_label': '210.d2', 'modell_image': '2B', 'prime': 2}
  • id: 888
    {'conductor': 210, 'elladic_image': '3.8.0.1', 'lmfdb_label': '210.d2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 210.d does not appear in ec_padic