Elliptic curve data - 2700.e1

Formats: - HTML - YAML - JSON - 2026-06-07T00:46:35.699869

• 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': '2700k', 'Clabel': '2700k1', 'Cnumber': 1, 'abc_quality': 0.646015014942309, 'absD': 486000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 30, 'ainvs': [0, 0, 0, 15, 25], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 2700, 'degree': 288, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.22294052879429211339011541154', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1], 'jinv': [768, 1], 'lmfdb_iso': '2700.e', 'lmfdb_label': '2700.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 15, 25], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['30.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.088335347692888813963756480466', 'prec': 107}, 'semistable': False, 'serre_invariants': [[2, 2, 135], [3, 8, 10], [5, 10, 108]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3141041873678446815940681340', 'prec': 103}, 'szpiro_ratio': 2.526373797161833, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 0, -2, 0, 0, 0, -2, 0, 6, 0, 0, 0, -1, 0, -3, 0], 'aplist': [0, 0, 0, -2, -2, 6, -1, -3, -7, 6, 1, -8, 10, -2, -8, -9, -10, 5, 8, -6, -2, 15, -13, -2, 8], 'class_deg': 1, 'class_size': 1, 'conductor': 2700, 'isogeny_matrix': [[1]], 'lmfdb_iso': '2700.e', 'trace_hash': 1928813917447956304}
• 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': '1.5618656834145240937915672317', 'prec': 100}, 'conductor': 2700, 'gens': [[5, 15, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.088335347692888813963756480466', 'prec': 107}], 'lmfdb_label': '2700.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9839338616449169150083955615', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1545267744257875233201231817398052225', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': [-1, 0, 5, 11, 65]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '2700.e1'}
• ec_torsion_growth •

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

  
  
  • id: 139564
    {'degree': 3, 'field': [-1, 3, 0, 1], 'lmfdb_label': '2700.e1', 'torsion': [2]}
  • id: 139565
    {'degree': 6, 'field': [1, -3, 3, -1, 3, -3, 1], 'lmfdb_label': '2700.e1', 'torsion': [2, 2]}
  • id: 139566
    {'degree': 8, 'field': [6, -31, 52, -33, -5, 23, -3, -4, 1], 'lmfdb_label': '2700.e1', 'torsion': [3]}
  • id: 139567
    {'degree': 12, 'field': [-375, 0, -2250, 0, -3675, 0, -750, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '2700.e1', 'torsion': [4]}
• 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: 47284
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '2700.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 47285
    {'conductor': 2700, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '2700.e1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 47286
    {'conductor': 2700, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '2700.e1', 'prime': 5, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 2, 0, 1], [1, 1, 29, 0], [1, 0, 2, 1], [7, 2, 7, 3], [11, 2, 11, 3], [29, 2, 28, 3]], 'adelic_image': '30.2.0.?', 'conductor': 2700, 'lmfdb_label': '2700.e1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 85300
    {'lmfdb_iso': '2700.e', 'p': 7, 'prec': 20, 'unit': 4604452819889256, 'val': 1}
  • id: 85301
    {'lmfdb_iso': '2700.e', 'p': 11, 'prec': 20, 'unit': 3002761667999151336, 'val': 2}
  • id: 85302
    {'lmfdb_iso': '2700.e', 'p': 13, 'prec': 20, 'unit': 306724304584116081320, 'val': 1}
  • id: 85303
    {'lmfdb_iso': '2700.e', 'p': 17, 'prec': 20, 'unit': 77831301751833294183303, 'val': 1}
  • id: 85304
    {'lmfdb_iso': '2700.e', 'p': 19, 'prec': 20, 'unit': 1117109118515749751619320, 'val': 1}
  • id: 85305
    {'lmfdb_iso': '2700.e', 'p': 23, 'prec': 20, 'unit': 57981814829968444156454449, 'val': 1}
  • id: 85306
    {'lmfdb_iso': '2700.e', 'p': 29, 'prec': 20, 'unit': 5865541709213940476978189574, 'val': 1}
  • id: 85307
    {'lmfdb_iso': '2700.e', 'p': 31, 'prec': 20, 'unit': 460369791156640520666581577167, 'val': -1}
  • id: 85308
    {'lmfdb_iso': '2700.e', 'p': 37, 'prec': 20, 'unit': 103641782697988462572129748803, 'val': 1}
  • id: 85309
    {'lmfdb_iso': '2700.e', 'p': 41, 'prec': 20, 'unit': 3760562520213994592319458980842, 'val': 1}
  • id: 85310
    {'lmfdb_iso': '2700.e', 'p': 43, 'prec': 20, 'unit': 8831440285090952949984644625003, 'val': 1}
  • id: 85311
    {'lmfdb_iso': '2700.e', 'p': 47, 'prec': 20, 'unit': 54403344704443530750611691651790, 'val': 1}
  • id: 85312
    {'lmfdb_iso': '2700.e', 'p': 53, 'prec': 20, 'unit': 262581656130499082150869444986514, 'val': 1}
  • id: 85313
    {'lmfdb_iso': '2700.e', 'p': 59, 'prec': 20, 'unit': 3442707864539543749503957783180004, 'val': 1}
  • id: 85314
    {'lmfdb_iso': '2700.e', 'p': 61, 'prec': 20, 'unit': 5797086938933355659992005536413061, 'val': 1}
  • id: 85315
    {'lmfdb_iso': '2700.e', 'p': 67, 'prec': 20, 'unit': 9210341247799619492150550781756323, 'val': 1}
  • id: 85316
    {'lmfdb_iso': '2700.e', 'p': 71, 'prec': 20, 'unit': 462076867368353039021319325180118, 'val': 2}
  • id: 85317
    {'lmfdb_iso': '2700.e', 'p': 73, 'prec': 20, 'unit': 17944947632748986208947887021664911, 'val': 1}
  • id: 85318
    {'lmfdb_iso': '2700.e', 'p': 79, 'prec': 20, 'unit': 823511743690363203639373905451668595, 'val': 1}
  • id: 85319
    {'lmfdb_iso': '2700.e', 'p': 83, 'prec': 20, 'unit': 439638345643366836942699515481536868, 'val': 1}
  • id: 85320
    {'lmfdb_iso': '2700.e', 'p': 89, 'prec': 20, 'unit': 3490011903819120195798037421003638976, 'val': 1}
  • id: 85321
    {'lmfdb_iso': '2700.e', 'p': 97, 'prec': 20, 'unit': 52543482204786671341531957372330375668, 'val': 1}