Elliptic curve data - 693.b2

Formats: - HTML - YAML - JSON - 2025-06-24T01:39:10.557104

• 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': '693c', 'Clabel': '693c2', 'Cnumber': 2, 'abc_quality': 1.0652168396120913, 'absD': 114154707051, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 1386, 'ainvs': [0, 0, 1, -444, -16650], 'analytic_rank': 0, 'bad_primes': [3, 7, 11], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 693, 'degree': 600, 'elladic_images': ['3.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.80361261928270555492016418371', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-13278380032, 156590819], 'lmfdb_iso': '693.b', 'lmfdb_label': '693.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -49, 600], 'min_quad_twist_disc': -3, 'modell_images': ['3Cs.1.1'], 'modm_images': ['3.24.0-3.a.1.1', '22.2.0.a.1', '63.72.0-63.b.1.1', '66.48.1-66.b.1.1', '1386.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 2, 1], [7, 8, 99], [11, 12, 63]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.25430647494865070922254156525', 'prec': 103}, 'szpiro_ratio': 5.039488658858358, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 0, 0, -2, -3, 0, 1, 0, 0, 0, 1, 0, -4, 0, 0, 4, 6, 0, 2, 6], 'aplist': [0, 0, -3, 1, 1, -4, 6, 2, -3, 6, 5, 11, -6, 8, 0, 6, 9, -10, 5, -9, 2, -10, -12, 3, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 693, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '693.b', 'trace_hash': 2287603757764489820}
• 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': '0.20044302472760550171235422019', 'prec': 103}, 'conductor': 693, 'gens': [], 'heights': [], 'lmfdb_label': '693.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44828619886164768437917383343', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.89657239772329536875834766685609605898', 'prec': 133}, 'tamagawa_product': 18, 'torsion_generators': [[48, 269, 1]], 'xcoord_integral_points': [48]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': 'a', '5': [0, 0], '7': [1, 0], '11': [1, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '693.b2'}
• ec_torsion_growth •

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

  
  
  • id: 32112
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '693.b2', 'torsion': [3, 3]}
  • id: 32113
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '693.b2', 'torsion': [6]}
  • id: 32114
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '693.b2', 'torsion': [2, 6]}
  • id: 32115
    {'degree': 6, 'field': [1, 1, 2, -3, 0, -1, 1], 'lmfdb_label': '693.b2', 'torsion': [3, 6]}
  • id: 32116
    {'degree': 9, 'field': [-216, -756, -2268, -2391, -441, -315, -18, -21, 0, 1], 'lmfdb_label': '693.b2', 'torsion': [9]}
  • id: 32117
    {'degree': 12, 'field': [-3179, 23122, -34240, 28914, -14629, 3036, 1056, -756, 135, -22, 16, -6, 1], 'lmfdb_label': '693.b2', 'torsion': [12]}
  • id: 32118
    {'degree': 12, 'field': [1, -1, -1, 4, -1, -3, 6, -3, -1, 4, -1, -1, 1], 'lmfdb_label': '693.b2', 'torsion': [6, 6]}
  • id: 32119
    {'degree': 18, 'field': [1, 0, 0, -28, 0, 0, 6010, 0, 0, -86, 0, 0, 37, 0, 0, -6, 0, 0, 1], 'lmfdb_label': '693.b2', 'torsion': [3, 9]}
  • id: 32120
    {'degree': 18, 'field': [7, 21, 21, 36, 48, 30, 25, -6, 30, -73, 99, -138, 151, -132, 114, -80, 36, -9, 1], 'lmfdb_label': '693.b2', 'torsion': [3, 9]}
  • id: 32121
    {'degree': 18, 'field': [592704, 0, 0, 144648, 0, 0, 49105, 0, 0, 6462, 0, 0, 1207, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '693.b2', 'torsion': [3, 9]}
• 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: 8574
    {'conductor': 693, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '693.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8575
    {'conductor': 693, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '693.b2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 8576
    {'conductor': 693, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '693.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1669070
    {'adelic_gens': [[262, 9, 873, 1378], [1, 18, 0, 1], [1, 9, 9, 82], [1, 6, 6, 37], [1385, 1368, 0, 1231], [1369, 18, 1368, 19], [1, 0, 18, 1], [1, 12, 0, 1], [7, 18, 1170, 463]], 'adelic_image': '1386.144.3.?', 'conductor': 693, 'lmfdb_label': '693.b2', 'prime': 0}
  • id: 3152
    {'conductor': 693, 'elladic_image': '3.24.0.1', 'lmfdb_label': '693.b2', 'modell_image': '3Cs.1.1', 'prime': 3}
• lmfdb_iso 693.b does not appear in ec_padic