Elliptic curve data - 277200.na1

Formats: - HTML - YAML - JSON - 2025-05-29T08:04:03.646455

• 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': '277200na', 'Clabel': '277200na6', 'Cnumber': 6, 'abc_quality': 1.00153318314077, 'absD': 7365772260000000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [0, 0, 0, -462006075, -3822254869750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 277200, 'degree': 37748736, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3701122674894397564820961649', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 338, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [467508233804095622882, 315748125], 'lmfdb_iso': '277200.na', 'lmfdb_label': '277200.na1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2053360, -1131835508], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '48.24.0.g.1', '56.24.0.bu.2', '60.12.0-4.c.1.2', '80.24.0.?', '88.24.0.?', '120.24.0.?', '240.48.0.?', '336.48.0.?', '528.48.0.?', '560.48.0.?', '616.48.0.?', '840.48.0.?', '880.48.0.?', '1320.48.0.?', '1680.96.0.?', '2640.96.0.?', '3696.96.1.?', '6160.96.0.?', '9240.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 17325], [3, 8, 30800], [5, 18, 11088], [7, 8, 39600], [11, 12, 25200]], 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3807022514250515231849644352', 'prec': 100}, 'szpiro_ratio': 5.702525428089311, '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, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, 0, 1, 1, 2, 2, -4, 0, 2, 8, 10, 6, -4, 0, -2, -12, 14, 12, 0, 6, 16, 4, 14, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 277200, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '277200.na', 'trace_hash': 517971897386020748}
• 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': '0.0011823816407711532244496373442', 'prec': 110}, 'conductor': 277200, 'gens': [], 'heights': [], 'lmfdb_label': '277200.na1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.032563991532569611294239288306', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1681909161689102456626289032307455493', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-12410, 0, 1]], 'xcoord_integral_points': [-12410]}
• lmfdb_label 277200.na1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11815547
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 2]}
  • id: 11815549
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '277200.na1', 'torsion': [4]}
  • id: 11815548
    {'degree': 2, 'field': [2310, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [4]}
  • id: 11815552
    {'degree': 4, 'field': [114, 6, -5, -2, 1], 'lmfdb_label': '277200.na1', 'torsion': [8]}
  • id: 11815551
    {'degree': 4, 'field': [654, 36, -35, -2, 1], 'lmfdb_label': '277200.na1', 'torsion': [8]}
  • id: 11815550
    {'degree': 4, 'field': [24810, 300, -299, -2, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 4]}
  • id: 11815553
    {'degree': 8, 'field': [152881, 0, -124380, 0, 118, 0, -60, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 4]}
  • id: 11815555
    {'degree': 8, 'field': [206376, 7440, -4052, -6676, 3089, 296, -94, -4, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 8]}
  • id: 11815556
    {'degree': 8, 'field': [1819599, -1864410, 383298, 18408, 4740, -2562, -140, -4, 1], 'lmfdb_label': '277200.na1', 'torsion': [6]}
  • id: 11815554
    {'degree': 8, 'field': [60388441, 0, 1344780, 0, 16442, 0, -60, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [8]}
  • id: 11815560
    {'degree': 16, 'field': [686336004, -1572377184, 1561788540, -1001394576, 595599678, -221438448, 103595574, -24266088, 9753049, -1289988, 506054, -31248, 14400, -252, 200, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [16]}
  • id: 11815557
    {'degree': 16, 'field': [707028100, 0, 367759280, 0, 72240956, 0, 4372032, 0, -44251, 0, 1596, 0, 974, 0, -28, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [4, 4]}
  • id: 11815559
    {'degree': 16, 'field': [17652505201, -33036101908, 46137962082, -22543636344, 25074005019, -3375130056, 3432566854, -297876292, 96942018, 11973180, -4994130, -187560, 69737, 1384, -426, -4, 1], 'lmfdb_label': '277200.na1', 'torsion': [16]}
  • id: 11815563
    {'degree': 16, 'field': [19936066896, -3391089408, 3725432784, -725846400, 504346680, -165606336, 48457984, 5588512, -1139655, -198760, 67340, -15672, 3158, -280, 60, -8, 1], 'lmfdb_label': '277200.na1', 'torsion': [12]}
  • id: 11815562
    {'degree': 16, 'field': [114040157298615, -148985465501700, 115352442897750, -47085243756300, 10125456945210, -1211398183620, 95914523064, -314396016, -1399840716, 55362684, 7901766, 498720, -956, -3476, 44, -4, 1], 'lmfdb_label': '277200.na1', 'torsion': [12]}
  • id: 11815558
    {'degree': 16, 'field': [3257059547987716, 0, 36244925292464, 0, 1859560192508, 0, 8025519936, 0, 331871333, 0, 208572, 0, 30542, 0, -28, 0, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 8]}
  • id: 11815561
    {'degree': 16, 'field': [218208618746576775, 80687137620955500, 8168711027285790, -835735664419020, -220464967175154, 357812255484, 2787271942584, 208428258720, 10401749700, 384371364, -20234034, -366144, -103520, -9020, 44, -4, 1], 'lmfdb_label': '277200.na1', 'torsion': [2, 6]}
• 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: 6867095
    {'conductor': 277200, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '277200.na1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6867096
    {'conductor': 277200, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '277200.na1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6867097
    {'conductor': 277200, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '277200.na1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6867098
    {'conductor': 277200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '277200.na1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6867099
    {'conductor': 277200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '277200.na1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 3414006
    {'adelic_gens': [[12319, 3680, 17240, 10959], [1, 16, 0, 1], [18465, 16, 18464, 17], [12776, 14785, 8815, 3706], [11549, 3680, 16170, 4619], [15, 2, 18382, 18467], [5, 4, 18476, 18477], [1, 0, 16, 1], [10576, 5, 2595, 18466], [13876, 10165, 13095, 12946], [14783, 0, 0, 18479]], 'adelic_image': '18480.192.1.?', 'conductor': 277200, 'lmfdb_label': '277200.na1', 'prime': 0}
  • id: 987673
    {'conductor': 277200, 'elladic_image': '8.12.0.5', 'lmfdb_label': '277200.na1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 277200.na does not appear in ec_padic