Elliptic curve data - 41650.s2

Formats: - HTML - YAML - JSON - 2025-10-25T20:46:12.962674

• 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': '41650p', 'Clabel': '41650p2', 'Cnumber': 2, 'abc_quality': 1.1339498614370396, 'absD': 5102209185062500, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 4760, 'ainvs': [1, -1, 0, -47392, 2001516], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 41650, 'degree': 196608, 'elladic_images': ['8.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7102295521213112611675228923', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [6403769793, 2775556], 'lmfdb_iso': '41650.s', 'lmfdb_label': '41650.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -39, -37], 'min_quad_twist_disc': -35, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0.a.1', '68.12.0.b.1', '136.24.0.?', '140.12.0.?', '280.24.0.?', '2380.24.0.?', '4760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2447933630791274784352149622', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1225], [5, 14, 1666], [7, 32, 850], [17, 18, 2450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.067444478623395578685533146035', 'prec': 110}, 'szpiro_ratio': 4.128232321007997, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 0, -1, -3, 0, 0, 0, -2, 0, 0, 1, 1, 3, -4, 0], 'aplist': [-1, 0, 0, 0, 0, -2, 1, -4, 0, -6, 0, 6, 6, 12, 8, 2, -4, -2, -12, 0, 2, -8, 12, -10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 41650, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '41650.s', 'trace_hash': 2084492820716018377}
• 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': '0.032697419968334902024553415026', 'prec': 107}, 'conductor': 41650, 'gens': [[214, 1168, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2447933630791274784352149622', 'prec': 100}], 'lmfdb_label': '41650.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38856587262999741035351275333', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4890003679954711167037740648020333149', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-236, 118, 1], [44, -22, 1]], 'xcoord_integral_points': [-236, -201, 44, 214, 3194]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [1, 5, 0], '5': 'a', '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '41650.s2'}
• ec_torsion_growth •

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

  
  
  • id: 2047420
    {'degree': 4, 'field': [119, -14, 15, -2, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 4]}
  • id: 2047419
    {'degree': 4, 'field': [676, 0, -18, 0, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 4]}
  • id: 2047418
    {'degree': 4, 'field': [926, 78, -77, -2, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 4]}
  • id: 2047421
    {'degree': 8, 'field': [-17204, -1411, 952, 917, -455, -7, 7, -4, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 6]}
  • id: 2047423
    {'degree': 16, 'field': [-1924639, -1419330, 10015212, 683494, 1065439, -693690, -291220, -102264, -42476, 3474, 2612, 2686, 455, 10, -44, -4, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 8]}
  • id: 2047422
    {'degree': 16, 'field': [323761, 0, 1364588, 0, 1139982, 0, -791792, 0, 399283, 0, 1264, 0, 1278, 0, -4, 0, 1], 'lmfdb_label': '41650.s2', 'torsion': [4, 4]}
  • id: 2047425
    {'degree': 16, 'field': [3625216, 0, -609280, 0, -221920, 0, -27648, 0, 14308, 0, -80, 0, 196, 0, 8, 0, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 8]}
  • id: 2047424
    {'degree': 16, 'field': [110206093804, -26075040944, -5914339128, -1600027648, 605695112, 489917080, -83867700, -33186784, 4909733, 1135880, -137880, -25016, 3122, 560, -60, -8, 1], 'lmfdb_label': '41650.s2', 'torsion': [2, 8]}
• 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: 988338
    {'conductor': 41650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '41650.s2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 988339
    {'conductor': 41650, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '41650.s2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 988340
    {'conductor': 41650, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '41650.s2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 988341
    {'conductor': 41650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '41650.s2', 'prime': 17, 'reduction_type': 1, '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: 1942106
    {'adelic_gens': [[1191, 140, 70, 281], [1, 0, 4, 1], [3399, 0, 0, 4759], [1, 4, 0, 1], [1903, 0, 0, 4759], [71, 2450, 2310, 2311], [3641, 140, 210, 281], [4757, 4, 4756, 5]], 'adelic_image': '4760.48.0.?', 'conductor': 41650, 'lmfdb_label': '41650.s2', 'prime': 0}
  • id: 182355
    {'conductor': 41650, 'elladic_image': '8.12.0.3', 'lmfdb_label': '41650.s2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2070262
    {'lmfdb_iso': '41650.s', 'p': 13, 'prec': 20, 'unit': 508980809323360107450, 'val': 1}
  • id: 2070265
    {'lmfdb_iso': '41650.s', 'p': 19, 'prec': 20, 'unit': 464696429801334622902738, 'val': 1}
  • id: 2070261
    {'lmfdb_iso': '41650.s', 'p': 29, 'prec': 20, 'unit': 663112327008457793714934931, 'val': 1}
  • id: 2070258
    {'lmfdb_iso': '41650.s', 'p': 37, 'prec': 20, 'unit': 216507245597421636644762332824, 'val': 1}
  • id: 2070259
    {'lmfdb_iso': '41650.s', 'p': 41, 'prec': 20, 'unit': 3476866772518421124901569478441, 'val': 1}
  • id: 2070260
    {'lmfdb_iso': '41650.s', 'p': 43, 'prec': 20, 'unit': 17329025974583134900227963542, 'val': 1}
  • id: 2070269
    {'lmfdb_iso': '41650.s', 'p': 47, 'prec': 20, 'unit': 41016059538536718072522638990814, 'val': 1}
  • id: 2070266
    {'lmfdb_iso': '41650.s', 'p': 53, 'prec': 20, 'unit': 114635958202481684946154021291883, 'val': 1}
  • id: 2070264
    {'lmfdb_iso': '41650.s', 'p': 59, 'prec': 20, 'unit': 417534104529613024949332559945648, 'val': 1}
  • id: 2070270
    {'lmfdb_iso': '41650.s', 'p': 61, 'prec': 20, 'unit': 2761829806173278580200302102458481, 'val': 1}
  • id: 2070257
    {'lmfdb_iso': '41650.s', 'p': 67, 'prec': 20, 'unit': 30440658128366409671006037992571248, 'val': 1}
  • id: 2070267
    {'lmfdb_iso': '41650.s', 'p': 73, 'prec': 20, 'unit': 76180878589799575031564823434640776, 'val': 1}
  • id: 2070263
    {'lmfdb_iso': '41650.s', 'p': 79, 'prec': 20, 'unit': 722825395992674480616589232808164396, 'val': 1}
  • id: 2070256
    {'lmfdb_iso': '41650.s', 'p': 83, 'prec': 20, 'unit': 2498106201491206740325295713749534616, 'val': 1}
  • id: 2070268
    {'lmfdb_iso': '41650.s', 'p': 89, 'prec': 20, 'unit': 8343994778602373006434986003804153005, 'val': 1}
  • id: 2070255
    {'lmfdb_iso': '41650.s', 'p': 97, 'prec': 20, 'unit': 31640135406439020076510200176233054498, 'val': 1}