Elliptic curve data - 51425.z1

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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': '51425s', 'Clabel': '51425s1', 'Cnumber': 1, 'abc_quality': 0.8484639388765889, 'absD': 11764272265625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 7480, 'ainvs': [1, 0, 1, -25776, 1582073], 'analytic_rank': 1, 'bad_primes': [5, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 51425, 'degree': 134400, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3459790820282122022687811607', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [68417929, 425], 'lmfdb_iso': '51425.z', 'lmfdb_label': '51425.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -8, -13], 'min_quad_twist_disc': -55, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '34.6.0.a.1', '68.12.0.e.1', '340.24.0.?', '440.12.0.?', '1496.24.0.?', '7480.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6152411476515885702168015641', 'prec': 100}, 'semistable': False, 'serre_invariants': [[5, 18, 2057], [11, 62, 425], [17, 18, 3025]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65768751058802325706257029489', 'prec': 107}, 'szpiro_ratio': 3.879573307140135, '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, 0, -2, -2, -3, 1, 0, 0, 2, 2, -2, 0, -1, 1, 1, 0, 0], 'aplist': [1, -2, 0, -2, 0, 2, 1, 0, -6, 6, -10, -2, -10, 4, -12, 10, 8, 14, -8, -2, -14, 14, 4, 6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 51425, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '51425.z', 'trace_hash': 1276472925078295229}
• 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': '0.067748147412819345304699194585', 'prec': 107}, 'conductor': 51425, 'gens': [[-741, 11, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '4.6152411476515885702168015641', 'prec': 100}], 'lmfdb_label': '51425.z1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.71894756481895581270362129313', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3181163841563524881858129914205284345', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[87, -44, 1]], 'xcoord_integral_points': [87]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [3, 0], '5': 'a', '7': [5, 0], '11': 'a', '13': [1, 0], '17': [2, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '51425.z1'}
• ec_torsion_growth •

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

  
  
  • id: 2492978
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '51425.z1', 'torsion': [2, 2]}
  • id: 2492979
    {'degree': 4, 'field': [3221, -110, -27, 0, 1], 'lmfdb_label': '51425.z1', 'torsion': [4]}
  • id: 2492982
    {'degree': 8, 'field': [-50041, 44255, -5623, -2076, -345, 201, -5, -2, 1], 'lmfdb_label': '51425.z1', 'torsion': [6]}
  • id: 2492980
    {'degree': 8, 'field': [74596, 19822, -15011, 6885, -55, 180, -71, -3, 1], 'lmfdb_label': '51425.z1', 'torsion': [2, 4]}
  • id: 2492981
    {'degree': 8, 'field': [591361, 0, 30777, 0, -1172, 0, -23, 0, 1], 'lmfdb_label': '51425.z1', 'torsion': [2, 4]}
  • id: 2492984
    {'degree': 16, 'field': [2141689801, -731962132, -565221814, 152790152, 61092648, -16375768, -596858, 505032, 54669, -53824, -1294, -800, 996, -108, 28, 0, 1], 'lmfdb_label': '51425.z1', 'torsion': [8]}
  • id: 2492983
    {'degree': 16, 'field': [2176129201, 0, 1449433184, 0, 488134322, 0, -33555948, 0, 2700571, 0, -98180, 0, 2986, 0, -76, 0, 1], 'lmfdb_label': '51425.z1', 'torsion': [4, 4]}
  • id: 2492985
    {'degree': 16, 'field': [3900627025, 0, 1871497625, 0, 139115275, 0, -35835570, 0, 1144665, 0, 24795, 0, -881, 0, -34, 0, 1], 'lmfdb_label': '51425.z1', '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: 1231243
    {'conductor': 51425, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '51425.z1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1231244
    {'conductor': 51425, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51425.z1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1231245
    {'conductor': 51425, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51425.z1', 'prime': 17, '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: 2005993
    {'adelic_gens': [[1, 8, 0, 1], [3741, 2728, 0, 1], [1, 0, 8, 1], [5, 8, 48, 77], [1871, 2728, 5104, 3433], [7473, 8, 7472, 9], [2806, 4081, 1463, 4764], [4079, 0, 0, 7479], [1, 4, 4, 17], [2441, 5434, 3542, 2045], [3, 8, 28, 75]], 'adelic_image': '7480.48.0.?', 'conductor': 51425, 'lmfdb_label': '51425.z1', 'prime': 0}
  • id: 220353
    {'conductor': 51425, 'elladic_image': '4.6.0.3', 'lmfdb_label': '51425.z1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2588206
    {'lmfdb_iso': '51425.z', 'p': 7, 'prec': 20, 'unit': 991959325529689, 'val': 2}
  • id: 2588210
    {'lmfdb_iso': '51425.z', 'p': 13, 'prec': 20, 'unit': 631892187916041368811, 'val': 1}
  • id: 2588216
    {'lmfdb_iso': '51425.z', 'p': 23, 'prec': 20, 'unit': 64392667534037513418313978, 'val': 1}
  • id: 2588209
    {'lmfdb_iso': '51425.z', 'p': 29, 'prec': 20, 'unit': 3517985881354657326434268505, 'val': 1}
  • id: 2588221
    {'lmfdb_iso': '51425.z', 'p': 31, 'prec': 20, 'unit': 17371019315661258492017616530, 'val': 1}
  • id: 2588205
    {'lmfdb_iso': '51425.z', 'p': 37, 'prec': 20, 'unit': 534819205978635905002528861850, 'val': 1}
  • id: 2588207
    {'lmfdb_iso': '51425.z', 'p': 41, 'prec': 20, 'unit': 10731351073293463284966004956, 'val': 2}
  • id: 2588208
    {'lmfdb_iso': '51425.z', 'p': 43, 'prec': 20, 'unit': 322541600269140821337407829764, 'val': 1}
  • id: 2588219
    {'lmfdb_iso': '51425.z', 'p': 47, 'prec': 20, 'unit': 32178383118772778647562823549404, 'val': 1}
  • id: 2588214
    {'lmfdb_iso': '51425.z', 'p': 53, 'prec': 20, 'unit': 210122432739722032937226989693698, 'val': 1}
  • id: 2588212
    {'lmfdb_iso': '51425.z', 'p': 59, 'prec': 20, 'unit': 1868328595939792710728121140087117, 'val': 1}
  • id: 2588220
    {'lmfdb_iso': '51425.z', 'p': 61, 'prec': 20, 'unit': 6450520310085731654160518971843519, 'val': 1}
  • id: 2588204
    {'lmfdb_iso': '51425.z', 'p': 67, 'prec': 20, 'unit': 24340241074782142649372816586149817, 'val': 1}
  • id: 2588218
    {'lmfdb_iso': '51425.z', 'p': 71, 'prec': 20, 'unit': 106944530015895984056426659213080197, 'val': 1}
  • id: 2588215
    {'lmfdb_iso': '51425.z', 'p': 73, 'prec': 20, 'unit': 117950998593066224556383088399769902, 'val': 1}
  • id: 2588211
    {'lmfdb_iso': '51425.z', 'p': 79, 'prec': 20, 'unit': 231147724152646046637206102268457127, 'val': 1}
  • id: 2588213
    {'lmfdb_iso': '51425.z', 'p': 83, 'prec': 20, 'unit': 720337874657121854001645488133507058, 'val': 1}
  • id: 2588217
    {'lmfdb_iso': '51425.z', 'p': 89, 'prec': 20, 'unit': 8172695512186064410406199314577525756, 'val': 1}
  • id: 2588203
    {'lmfdb_iso': '51425.z', 'p': 97, 'prec': 20, 'unit': 5004744383154519767901394444442031864, 'val': 1}