Elliptic curve data - 61370.x2

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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': '61370x', 'Clabel': '61370x2', 'Cnumber': 2, 'abc_quality': 0.9103514678397865, 'absD': 33990649022500, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 12920, 'ainvs': [1, 1, 1, 4505, -253343], 'analytic_rank': 1, 'bad_primes': [2, 5, 17, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 61370, 'degree': 193536, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2795021914291396069620913871', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [214921799, 722500], 'lmfdb_iso': '61370.x', 'lmfdb_label': '61370.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 12, 38], 'min_quad_twist_disc': -19, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '68.12.0.d.1', '76.12.0.?', '680.24.0.?', '1292.24.0.?', '12920.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.4464342109066471207229684785', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 361], [5, 6, 12274], [17, 18, 3610], [19, 182, 170]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19271729815408062304242232884', 'prec': 107}, 'szpiro_ratio': 3.485173237470725, '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, 2, 1, 1, 2, -2, 1, 1, 1, -2, 2, 6, -2, 2, 1, 1, 1, 0, 1], 'aplist': [1, 2, 1, -2, -2, 6, 1, 0, -2, -6, 2, -6, -2, -4, 4, 10, 0, -10, -8, -14, 10, 14, -4, -6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 61370, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '61370.x', 'trace_hash': 2281257982345679285}
• 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': '0.077381744695036984471912744592', 'prec': 107}, 'conductor': 61370, 'gens': [[775, 21763, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '5.4464342109066471207229684785', 'prec': 100}], 'lmfdb_label': '61370.x2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33388282428227334688632330619', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '14.547766692840849234777953523299202146', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[163, -167, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': [1, 0], '5': [4, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [4, 0], '19': 'a', '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '61370.x2'}
• ec_torsion_growth •

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

  
  
  • id: 2942627
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '61370.x2', 'torsion': [2, 2]}
  • id: 2942628
    {'degree': 4, 'field': [-94, 39, 3, -1, 1], 'lmfdb_label': '61370.x2', 'torsion': [4]}
  • id: 2942629
    {'degree': 8, 'field': [676, 0, -392, 0, 133, 0, -18, 0, 1], 'lmfdb_label': '61370.x2', 'torsion': [2, 4]}
  • id: 2942630
    {'degree': 8, 'field': [8836, 0, 2085, 0, -101, 0, -5, 0, 1], 'lmfdb_label': '61370.x2', 'torsion': [2, 4]}
  • id: 2942631
    {'degree': 8, 'field': [21080, -50320, 11900, -766, 1022, -256, 1, -2, 1], 'lmfdb_label': '61370.x2', 'torsion': [6]}
  • id: 2942632
    {'degree': 16, 'field': [1763584, 0, -1302800, 0, 532257, 0, -153888, 0, 30784, 0, -4362, 0, 440, 0, -28, 0, 1], 'lmfdb_label': '61370.x2', 'torsion': [4, 4]}
  • id: 2942633
    {'degree': 16, 'field': [376512124, -800059440, 576671552, -125737576, -31008511, 18305844, -8101194, 2062860, -217045, 6312, 18452, -32, 663, -44, 54, -4, 1], 'lmfdb_label': '61370.x2', 'torsion': [8]}
  • id: 2942634
    {'degree': 16, 'field': [444366400, 0, 2030398400, 0, 107607280, 0, 1984836, 0, 516972, 0, 42756, 0, 1021, 0, 2, 0, 1], 'lmfdb_label': '61370.x2', '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: 1479692
    {'conductor': 61370, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '61370.x2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1479693
    {'conductor': 61370, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '61370.x2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1479694
    {'conductor': 61370, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '61370.x2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1479695
    {'conductor': 61370, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '61370.x2', 'prime': 19, '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: 2070959
    {'adelic_gens': [[2281, 6802, 0, 1], [3, 8, 10, 27], [6461, 1368, 0, 1], [3231, 1368, 11647, 2737], [12913, 8, 12912, 9], [1, 0, 8, 1], [1, 8, 0, 1], [10337, 684, 0, 1], [5, 8, 48, 77], [3399, 0, 0, 12919]], 'adelic_image': '12920.48.0.?', 'conductor': 61370, 'lmfdb_label': '61370.x2', 'prime': 0}
  • id: 258813
    {'conductor': 61370, 'elladic_image': '4.6.0.5', 'lmfdb_label': '61370.x2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3119795
    {'lmfdb_iso': '61370.x', 'p': 7, 'prec': 20, 'unit': 159113408313259, 'val': 1}
  • id: 3119793
    {'lmfdb_iso': '61370.x', 'p': 11, 'prec': 20, 'unit': 59384343132571328486, 'val': 1}
  • id: 3119799
    {'lmfdb_iso': '61370.x', 'p': 13, 'prec': 20, 'unit': 689949496868377444147, 'val': 1}
  • id: 3119804
    {'lmfdb_iso': '61370.x', 'p': 23, 'prec': 20, 'unit': 22224376345586436580115890, 'val': 1}
  • id: 3119798
    {'lmfdb_iso': '61370.x', 'p': 29, 'prec': 20, 'unit': 136680550433643501112189001, 'val': 2}
  • id: 3119809
    {'lmfdb_iso': '61370.x', 'p': 31, 'prec': 20, 'unit': 5945427814320560626328487679, 'val': 1}
  • id: 3119794
    {'lmfdb_iso': '61370.x', 'p': 37, 'prec': 20, 'unit': 363216725610693465829153129508, 'val': 1}
  • id: 3119796
    {'lmfdb_iso': '61370.x', 'p': 41, 'prec': 20, 'unit': 2307392031940881693406838676084, 'val': 1}
  • id: 3119797
    {'lmfdb_iso': '61370.x', 'p': 43, 'prec': 20, 'unit': 6607233568166283726073555009959, 'val': 1}
  • id: 3119800
    {'lmfdb_iso': '61370.x', 'p': 47, 'prec': 20, 'unit': 13011548437348837027372067040903, 'val': 1}
  • id: 3119802
    {'lmfdb_iso': '61370.x', 'p': 53, 'prec': 20, 'unit': 395428701021003531944891749721308, 'val': 1}
  • id: 3119808
    {'lmfdb_iso': '61370.x', 'p': 61, 'prec': 20, 'unit': 918571459185381030491362037701021, 'val': 1}
  • id: 3119801
    {'lmfdb_iso': '61370.x', 'p': 67, 'prec': 20, 'unit': 13836630721750601154429302252681927, 'val': 1}
  • id: 3119806
    {'lmfdb_iso': '61370.x', 'p': 71, 'prec': 20, 'unit': 107778641864734695997527242988801984, 'val': 1}
  • id: 3119803
    {'lmfdb_iso': '61370.x', 'p': 73, 'prec': 20, 'unit': 218212001645305951318754483496081690, 'val': 1}
  • id: 3119807
    {'lmfdb_iso': '61370.x', 'p': 79, 'prec': 20, 'unit': 972673384750184858185606491604614858, 'val': 1}
  • id: 3119792
    {'lmfdb_iso': '61370.x', 'p': 83, 'prec': 20, 'unit': 1837541171038357373178452349488449940, 'val': 1}
  • id: 3119805
    {'lmfdb_iso': '61370.x', 'p': 89, 'prec': 20, 'unit': 434484286781616755735086063168970141, 'val': 1}
  • id: 3119791
    {'lmfdb_iso': '61370.x', 'p': 97, 'prec': 20, 'unit': 17965198336225013523387615770512791754, 'val': 1}