Elliptic curve data - 76230.ee1

Formats: - HTML - YAML - JSON - 2025-10-20T17:24:08.200602

• 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': '76230ej', 'Clabel': '76230ej7', 'Cnumber': 7, 'abc_quality': 1.0344564436307178, 'absD': 3095388168030254250, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [1, -1, 1, -5797837112, -169919579126239], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 76230, 'degree': 39813120, 'elladic_images': ['4.12.0.8', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8706754119346698826535480644', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 108, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16689299266861680229173649, 2396798250], 'lmfdb_iso': '76230.ee', 'lmfdb_label': '76230.ee1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5324001, -4728746769], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.12.0-4.c.1.2', '6.12.0.a.1', '12.48.0-12.g.1.7', '33.8.0-3.a.1.2', '66.24.0-6.a.1.2', '120.96.0.?', '132.96.0.?', '168.96.0.?', '280.24.0.?', '840.192.1.?', '1320.192.1.?', '1848.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '27.457428783017232104125648217', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 5445], [3, 8, 1694], [5, 6, 15246], [7, 8, 10890], [11, 72, 630]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1224216312014297649249536570', 'prec': 100}, 'szpiro_ratio': 7.032494103150137, '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, 0, 1, 1, 0, -1, 1, 0, 1, 0, 0, -2, -1, 0, 1, 6, 0, 4, 1], 'aplist': [1, 0, 1, -1, 0, -2, 6, 4, 0, 6, 8, -10, -6, -8, 0, -6, -12, -2, -4, -12, 10, 4, -12, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 76230, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '76230.ee', 'trace_hash': 1422321506294246713}
• 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': '0.00043448426677458893439756204063', 'prec': 113}, 'conductor': 76230, 'gens': [[612512183251, 331598121024005643, 2278]], 'heights': [{'__RealLiteral__': 0, 'data': '27.457428783017232104125648217', 'prec': 100}], 'lmfdb_label': '76230.ee1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.017301471919413664967628313233', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.401294393648155881551649424017309607', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-175845, 175841, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': 'a', '5': [2, 0], '7': [1, 0], '11': 'a', '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': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '76230.ee1'}
• ec_torsion_growth •

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

  
  
  • id: 3606067
    {'degree': 2, 'field': [-330, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 2]}
  • id: 3606068
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [4]}
  • id: 3606070
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '76230.ee1', 'torsion': [6]}
  • id: 3606069
    {'degree': 2, 'field': [330, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [4]}
  • id: 3606071
    {'degree': 4, 'field': [-74250, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 4]}
  • id: 3606074
    {'degree': 4, 'field': [9, 0, -5, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [12]}
  • id: 3606073
    {'degree': 4, 'field': [759, -66, 67, -2, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 6]}
  • id: 3606075
    {'degree': 4, 'field': [1059, 54, -53, -2, 1], 'lmfdb_label': '76230.ee1', 'torsion': [12]}
  • id: 3606072
    {'degree': 4, 'field': [27225, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 4]}
  • id: 3606076
    {'degree': 6, 'field': [2302, -2334, 294, -37, -21, -3, 1], 'lmfdb_label': '76230.ee1', 'torsion': [6]}
  • id: 3606081
    {'degree': 8, 'field': [52281, 7092, -6588, -1020, 541, -40, 18, -4, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 12]}
  • id: 3606078
    {'degree': 8, 'field': [132496, 0, -23492, 0, 1689, 0, -62, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [8]}
  • id: 3606079
    {'degree': 8, 'field': [810000, 0, 0, 0, 1170, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [8]}
  • id: 3606080
    {'degree': 8, 'field': [1733241, -42348, 39762, 5160, -2549, -40, 18, -4, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 12]}
  • id: 3606077
    {'degree': 8, 'field': [1594484761, 0, -479156, 0, 79866, 0, 4, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [4, 4]}
  • id: 3606083
    {'degree': 12, 'field': [-73083996, -20048256, 2962872, 1757940, 1288278, -241920, -10331, -15918, 3561, 352, -93, -6, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 6]}
  • id: 3606082
    {'degree': 12, 'field': [4524129, -1397439, 623079, -217380, 25281, 3537, 7588, -417, 429, -166, -3, -3, 1], 'lmfdb_label': '76230.ee1', 'torsion': [3, 6]}
  • id: 3606084
    {'degree': 12, 'field': [6282676, 10153584, 5125164, 387660, -202116, 56196, 22025, 0, 1059, -168, 51, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [12]}
  • id: 3606085
    {'degree': 12, 'field': [12165124, 33456480, 21454488, -3170596, 2030370, -727248, 23261, -2814, 429, 88, 27, -6, 1], 'lmfdb_label': '76230.ee1', 'torsion': [12]}
  • id: 3606090
    {'degree': 16, 'field': [5764801, 0, 0, 0, 153664, 0, 0, 0, 339390, 0, 0, 0, 64, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [24]}
  • id: 3606091
    {'degree': 16, 'field': [100000000, 0, 0, 0, 29900000, 0, 0, 0, 5286900, 0, 0, 0, 2990, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [24]}
  • id: 3606087
    {'degree': 16, 'field': [5522570596, -115335328, 1204352, 227946264, -112433104, -3948752, 4811272, -2978532, 712237, 38508, -24536, 9068, -1390, -84, 32, -8, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 8]}
  • id: 3606089
    {'degree': 16, 'field': [12385686681, 0, 2276747820, 0, 292089486, 0, 11857440, 0, 404431, 0, 5560, 0, 1506, 0, -20, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [4, 12]}
  • id: 3606088
    {'degree': 16, 'field': [657998391241, 0, -11412289072, 0, 2016973648, 0, -39949864, 0, 2949190, 0, -4624, 0, 2368, 0, 8, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 8]}
  • id: 3606086
    {'degree': 16, 'field': [9123405592910400, 0, 0, 0, -34704363513600, 0, 0, 0, 3656186160, 0, 0, 0, -47520, 0, 0, 0, 1], 'lmfdb_label': '76230.ee1', 'torsion': [2, 8]}
  • id: 3606092
    {'degree': 18, 'field': [4618207907533575, -1930837708180800, -64779179278950, 131068766907705, -4410819189765, -3227292352170, 117028556358, 24105943449, 2956488900, 1004006119, 187710705, 23686569, 375431, -42627, -1437, -1930, 21, -9, 1], 'lmfdb_label': '76230.ee1', 'torsion': [18]}
• 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: 1854256
    {'conductor': 76230, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '76230.ee1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1854257
    {'conductor': 76230, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '76230.ee1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1854258
    {'conductor': 76230, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '76230.ee1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1854259
    {'conductor': 76230, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '76230.ee1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1854260
    {'conductor': 76230, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '76230.ee1', 'prime': 11, '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

  
  
  • id: 2167749
    {'adelic_gens': [[1, 24, 0, 1], [1, 0, 24, 1], [1, 12, 12, 145], [5864, 9237, 2139, 86], [2311, 24, 2310, 1], [4242, 2719, 7037, 6692], [9217, 24, 9216, 25], [3712, 21, 8955, 8866], [5281, 24, 7932, 289], [6144, 7681, 5575, 1134], [15, 106, 7934, 11]], 'adelic_image': '9240.384.5.?', 'conductor': 76230, 'lmfdb_label': '76230.ee1', 'prime': 0}
  • id: 314990
    {'conductor': 76230, 'elladic_image': '4.12.0.8', 'lmfdb_label': '76230.ee1', 'modell_image': '2B', 'prime': 2}
  • id: 314991
    {'conductor': 76230, 'elladic_image': '3.4.0.1', 'lmfdb_label': '76230.ee1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3924788
    {'lmfdb_iso': '76230.ee', 'p': 13, 'prec': 20, 'unit': 1205372929782142624016, 'val': 1}
  • id: 3924790
    {'lmfdb_iso': '76230.ee', 'p': 17, 'prec': 20, 'unit': 191207932139888770891620, 'val': 1}
  • id: 3924780
    {'lmfdb_iso': '76230.ee', 'p': 19, 'prec': 20, 'unit': 1557950821738508944322674, 'val': 1}
  • id: 3924787
    {'lmfdb_iso': '76230.ee', 'p': 29, 'prec': 20, 'unit': 582288380871609348428129083, 'val': 1}
  • id: 3924797
    {'lmfdb_iso': '76230.ee', 'p': 31, 'prec': 20, 'unit': 10221497756619811731470325051, 'val': 1}
  • id: 3924783
    {'lmfdb_iso': '76230.ee', 'p': 37, 'prec': 20, 'unit': 436829626281874114951679248140, 'val': 1}
  • id: 3924785
    {'lmfdb_iso': '76230.ee', 'p': 41, 'prec': 20, 'unit': 133385049209571446598017237675, 'val': 1}
  • id: 3924786
    {'lmfdb_iso': '76230.ee', 'p': 43, 'prec': 20, 'unit': 3668863404708912534804541053833, 'val': 1}
  • id: 3924792
    {'lmfdb_iso': '76230.ee', 'p': 53, 'prec': 20, 'unit': 359459221599111867857284071745153, 'val': 1}
  • id: 3924795
    {'lmfdb_iso': '76230.ee', 'p': 59, 'prec': 20, 'unit': 812810173578829753103070243678897, 'val': 1}
  • id: 3924796
    {'lmfdb_iso': '76230.ee', 'p': 61, 'prec': 20, 'unit': 1580538415897206417591254909663748, 'val': 1}
  • id: 3924782
    {'lmfdb_iso': '76230.ee', 'p': 67, 'prec': 20, 'unit': 24394318936692592093483354382357209, 'val': 1}
  • id: 3924784
    {'lmfdb_iso': '76230.ee', 'p': 71, 'prec': 20, 'unit': 143724377307079618168495120964633994, 'val': 1}
  • id: 3924793
    {'lmfdb_iso': '76230.ee', 'p': 73, 'prec': 20, 'unit': 251372808574268812427596915525842453, 'val': 1}
  • id: 3924789
    {'lmfdb_iso': '76230.ee', 'p': 79, 'prec': 20, 'unit': 590508666870675839632461006956109665, 'val': 1}
  • id: 3924791
    {'lmfdb_iso': '76230.ee', 'p': 83, 'prec': 20, 'unit': 1259668804704163320103665306030707315, 'val': 1}
  • id: 3924794
    {'lmfdb_iso': '76230.ee', 'p': 89, 'prec': 20, 'unit': 5071116346174844145525251754664887407, 'val': 1}
  • id: 3924781
    {'lmfdb_iso': '76230.ee', 'p': 97, 'prec': 20, 'unit': 23143912210888458101442333025211685637, 'val': 1}