Elliptic curve data - 49686.cn2

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• 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': '49686ck', 'Clabel': '49686ck2', 'Cnumber': 2, 'abc_quality': 1.0580983204947527, 'absD': 3002184304164864, 'adelic_genus': 0, 'adelic_index': 32, 'adelic_level': 2184, 'ainvs': [1, 1, 1, 25626, 2121699], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 49686, 'degree': 414720, 'elladic_images': ['4.2.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6549881954898990607625856631', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 65, 'isogeny_degrees': [1, 3], 'jinv': [93603087383, 150994944], 'lmfdb_iso': '49686.cn', 'lmfdb_label': '49686.cn2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 523, -6111], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '4.2.0.a.1', '12.8.0.a.1', '24.16.0.b.1', '273.8.0.?', '1092.16.0.?', '2184.32.0.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.31489311957400443340401773584', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 8281], [3, 4, 8281], [7, 26, 1014], [13, 38, 294]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.25454156138531961886766138445', 'prec': 103}, 'szpiro_ratio': 3.9440140198328306, '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, 1, -1, 1, 3, -1, 0, 1, 1, 3, -6, -1, 0, 0, -3, 1, 3, 1, 2, 3], 'aplist': [1, -1, 3, 0, -6, 0, 3, 2, -6, 3, -4, 7, -3, -10, 6, 3, 0, 7, 10, -6, -13, -4, -6, 18, 14], 'class_deg': 3, 'class_size': 2, 'conductor': 49686, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '49686.cn', 'trace_hash': 2203788921059685314}
• 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': '0.036517035875001128563623832106', 'prec': 107}, 'conductor': 49686, 'gens': [[97, 2303, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.31489311957400443340401773584', 'prec': 103}], 'lmfdb_label': '49686.cn2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.30743139918893390513437919388', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.2935711051780275623676655108722426717', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [], 'xcoord_integral_points': [-63, 97, 1457]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [11, 0], '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': 'a', '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': '49686.cn2'}
• ec_torsion_growth •

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

  
  
  • id: 2416300
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '49686.cn2', 'torsion': [3]}
  • id: 2416301
    {'degree': 3, 'field': [12, -4, -1, 1], 'lmfdb_label': '49686.cn2', 'torsion': [2]}
  • id: 2416304
    {'degree': 6, 'field': [-4928, -3136, 1436, 134, -70, -1, 1], 'lmfdb_label': '49686.cn2', 'torsion': [6]}
  • id: 2416302
    {'degree': 6, 'field': [8, -20, 25, -6, 2, -2, 1], 'lmfdb_label': '49686.cn2', 'torsion': [2, 2]}
  • id: 2416303
    {'degree': 6, 'field': [16340, -6852, 1539, -61, 72, -3, 1], 'lmfdb_label': '49686.cn2', 'torsion': [3]}
  • id: 2416305
    {'degree': 12, 'field': [713232, -2020122, 1560312, -599235, 182949, -60814, 34982, -9790, 174, 420, -58, -3, 1], 'lmfdb_label': '49686.cn2', 'torsion': [4]}
  • id: 2416306
    {'degree': 12, 'field': [23765625, 0, 0, 0, 0, 0, -7722, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '49686.cn2', 'torsion': [3, 3]}
  • id: 2416307
    {'degree': 12, 'field': [24285184, 0, 23987712, 0, 3592464, 0, 235124, 0, 8040, 0, 141, 0, 1], 'lmfdb_label': '49686.cn2', 'torsion': [2, 6]}
  • id: 2416308
    {'degree': 18, 'field': [-9401993600, 5945158080, 20998959552, -27643720792, 11113241544, -1261433760, 130013146, -205390230, 66588102, -9622219, 1745967, -19128, -102454, 1134, 3486, 198, -96, -3, 1], 'lmfdb_label': '49686.cn2', 'torsion': [9]}
  • id: 2416309
    {'degree': 18, 'field': [85245952, -369954816, 688567296, -718985216, 498105216, -255340416, 103639056, -32857728, 10220952, -2863440, 875136, -213708, 48510, -8484, 1899, -229, 66, -3, 1], 'lmfdb_label': '49686.cn2', 'torsion': [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: 1188716
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '49686.cn2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 24}
  • id: 1188717
    {'conductor': 49686, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49686.cn2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1188718
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '49686.cn2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1188719
    {'conductor': 49686, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '49686.cn2', 'prime': 13, 'reduction_type': 0, '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: 1994745
    {'adelic_gens': [[5, 2, 2146, 2169], [1, 0, 12, 1], [1093, 945, 1407, 652], [4, 9, 3, 7], [57, 1253, 1015, 316], [1, 12, 0, 1], [365, 945, 1771, 652], [2173, 12, 2172, 13], [547, 1260, 273, 1], [935, 0, 0, 2183]], 'adelic_image': '2184.32.0.?', 'conductor': 49686, 'lmfdb_label': '49686.cn2', 'prime': 0}
  • id: 213814
    {'conductor': 49686, 'elladic_image': '4.2.0.1', 'lmfdb_label': '49686.cn2', 'modell_image': '2G', 'prime': 2}
  • id: 213815
    {'conductor': 49686, 'elladic_image': '3.4.0.1', 'lmfdb_label': '49686.cn2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2496702
    {'lmfdb_iso': '49686.cn', 'p': 5, 'prec': 20, 'unit': 3792116314899, 'val': 1}
  • id: 2496709
    {'lmfdb_iso': '49686.cn', 'p': 11, 'prec': 20, 'unit': 13664787646735225475, 'val': 1}
  • id: 2496710
    {'lmfdb_iso': '49686.cn', 'p': 17, 'prec': 20, 'unit': 230653387017851907064418, 'val': 1}
  • id: 2496711
    {'lmfdb_iso': '49686.cn', 'p': 19, 'prec': 20, 'unit': 1222085565328777436810683, 'val': 1}
  • id: 2496714
    {'lmfdb_iso': '49686.cn', 'p': 23, 'prec': 20, 'unit': 64473439974670296129768204, 'val': 1}
  • id: 2496707
    {'lmfdb_iso': '49686.cn', 'p': 29, 'prec': 20, 'unit': 3592445696751412723641290758, 'val': 1}
  • id: 2496704
    {'lmfdb_iso': '49686.cn', 'p': 31, 'prec': 20, 'unit': 10237059521503252710454172458, 'val': 1}
  • id: 2496718
    {'lmfdb_iso': '49686.cn', 'p': 37, 'prec': 20, 'unit': 155726001824180982181057190281, 'val': 1}
  • id: 2496705
    {'lmfdb_iso': '49686.cn', 'p': 41, 'prec': 20, 'unit': 4073674315790933349321009476067, 'val': 1}
  • id: 2496706
    {'lmfdb_iso': '49686.cn', 'p': 43, 'prec': 20, 'unit': 5784554060167617905245210745820, 'val': 1}
  • id: 2496708
    {'lmfdb_iso': '49686.cn', 'p': 47, 'prec': 20, 'unit': 37255797519735379941749528719248, 'val': 1}
  • id: 2496712
    {'lmfdb_iso': '49686.cn', 'p': 53, 'prec': 20, 'unit': 486690490374924489012232725074810, 'val': 1}
  • id: 2496717
    {'lmfdb_iso': '49686.cn', 'p': 61, 'prec': 20, 'unit': 1993090016974747351622861639989988, 'val': 1}
  • id: 2496701
    {'lmfdb_iso': '49686.cn', 'p': 67, 'prec': 20, 'unit': 24636159303617569055191401102240840, 'val': 1}
  • id: 2496703
    {'lmfdb_iso': '49686.cn', 'p': 71, 'prec': 20, 'unit': 27137580382050807907377621770209995, 'val': 1}
  • id: 2496713
    {'lmfdb_iso': '49686.cn', 'p': 73, 'prec': 20, 'unit': 185653542814496354170764537703849395, 'val': 1}
  • id: 2496716
    {'lmfdb_iso': '49686.cn', 'p': 79, 'prec': 20, 'unit': 467724323727870799714191615601011759, 'val': 1}
  • id: 2496700
    {'lmfdb_iso': '49686.cn', 'p': 83, 'prec': 20, 'unit': 973806651630424458443352424448687914, 'val': 1}
  • id: 2496715
    {'lmfdb_iso': '49686.cn', 'p': 89, 'prec': 20, 'unit': 2977982520965568630624364204085179509, 'val': 1}
  • id: 2496699
    {'lmfdb_iso': '49686.cn', 'p': 97, 'prec': 20, 'unit': 49821126710991774491834162380615958059, 'val': 1}