Elliptic curve data - 25215.i2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '25215g', 'Clabel': '25215g2', 'Cnumber': 2, 'abc_quality': 1.1547638000559055, 'absD': 352317969757428581297025, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 1640, 'ainvs': [1, 0, 1, -231173, -28557902347], 'analytic_rank': 1, 'bad_primes': [3, 5, 41], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 25215, 'degree': 3358720, 'elladic_images': ['8.12.0.27'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1971208982063797227458489136', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [-4173281, 1076168025], 'lmfdb_iso': '25215.i', 'lmfdb_label': '25215.i2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -137, -414414], 'min_quad_twist_disc': 41, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '8.12.0.r.1', '40.24.0.dk.1', '164.12.0.?', '328.24.0.?', '1640.48.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.038730987442165340865073275', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 41], [3, 4, 8405], [5, 6, 5043], [41, 482, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41194184817814886984577638382', 'prec': 97}, 'szpiro_ratio': 6.0850873897323075, '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, 1, -1, 1, 1, -4, -3, 1, 1, 0, -1, 4, -4, 1, -1, -4, 1, 0, -1], 'aplist': [1, 1, 1, -4, 0, 4, -4, 0, 0, 8, -8, -6, 0, 12, -4, 12, 4, -14, -12, 8, 10, -8, 4, 8, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 25215, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '25215.i', 'trace_hash': 2217833066306247262}
• 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': '0.0016711524572241339719443630911', 'prec': 97}, 'conductor': 25215, 'gens': [[318669, 178876945, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '10.038730987442165340865073275', 'prec': 97}], 'lmfdb_label': '25215.i2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.043816859074573233399394398271', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0378505754288761336900711336098729563', 'prec': 127}, 'tamagawa_product': 64, 'torsion_generators': [[12327, -12331, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 1], '3': [4, 0], '5': [2, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': 'a', '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '25215.i2'}
• ec_torsion_growth •

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

  
  
  • id: 1270288
    {'degree': 2, 'field': [41, 0, 1], 'lmfdb_label': '25215.i2', 'torsion': [2, 2]}
  • id: 1270289
    {'degree': 4, 'field': [-41, 0, 0, 0, 1], 'lmfdb_label': '25215.i2', 'torsion': [4]}
  • id: 1270294
    {'degree': 8, 'field': [-134525, 21425, -22670, 2489, -1241, -7, 7, -4, 1], 'lmfdb_label': '25215.i2', 'torsion': [6]}
  • id: 1270290
    {'degree': 8, 'field': [100, 20, 2, -46, 29, -10, 8, -4, 1], 'lmfdb_label': '25215.i2', 'torsion': [2, 4]}
  • id: 1270292
    {'degree': 8, 'field': [6889, 0, -8820, 0, 814, 0, -36, 0, 1], 'lmfdb_label': '25215.i2', 'torsion': [8]}
  • id: 1270293
    {'degree': 8, 'field': [8100, -5130, 4599, -1395, 617, -110, 35, -3, 1], 'lmfdb_label': '25215.i2', 'torsion': [8]}
  • id: 1270291
    {'degree': 8, 'field': [69696, 0, 15680, 0, 928, 0, -40, 0, 1], 'lmfdb_label': '25215.i2', 'torsion': [2, 4]}
  • id: 1270296
    {'degree': 16, 'field': [2025, 0, 193140, 0, 141046, 0, 37904, 0, 23943, 0, 6880, 0, 798, 0, 44, 0, 1], 'lmfdb_label': '25215.i2', 'torsion': [2, 8]}
  • id: 1270295
    {'degree': 16, 'field': [96100, -620000, 2000000, -1698920, 634944, 299456, -128888, 88892, -10187, -6652, 1576, -244, 42, -44, 32, -8, 1], 'lmfdb_label': '25215.i2', 'torsion': [4, 4]}
  • id: 1270297
    {'degree': 16, 'field': [19793601, 0, 35890002, 0, 7899921, 0, 2026649, 0, 86696, 0, 19511, 0, -164, 0, 28, 0, 1], 'lmfdb_label': '25215.i2', '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: 579726
    {'conductor': 25215, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '25215.i2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 579727
    {'conductor': 25215, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '25215.i2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 579728
    {'conductor': 25215, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '25215.i2', 'prime': 41, '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: 1832458
    {'adelic_gens': [[5, 2, 1334, 9], [3, 8, 1632, 1619], [48, 3, 357, 1624], [1, 0, 8, 1], [5, 8, 48, 77], [1, 418, 410, 1], [1633, 8, 1632, 9], [1236, 429, 813, 388], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1640.48.1.?', 'conductor': 25215, 'lmfdb_label': '25215.i2', 'prime': 0}
  • id: 115051
    {'conductor': 25215, 'elladic_image': '8.12.0.27', 'lmfdb_label': '25215.i2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1200604
    {'lmfdb_iso': '25215.i', 'p': 7, 'prec': 20, 'unit': 9480653661513212, 'val': 1}
  • id: 1200608
    {'lmfdb_iso': '25215.i', 'p': 13, 'prec': 20, 'unit': 1009130377480766236054, 'val': 1}
  • id: 1200610
    {'lmfdb_iso': '25215.i', 'p': 17, 'prec': 20, 'unit': 449196387848346827606, 'val': 1}
  • id: 1200607
    {'lmfdb_iso': '25215.i', 'p': 29, 'prec': 20, 'unit': 4857040000481570394443929050, 'val': 1}
  • id: 1200618
    {'lmfdb_iso': '25215.i', 'p': 31, 'prec': 20, 'unit': 6818348041005794558047686278, 'val': 1}
  • id: 1200603
    {'lmfdb_iso': '25215.i', 'p': 37, 'prec': 20, 'unit': 163855024807252290642312844213, 'val': 1}
  • id: 1200606
    {'lmfdb_iso': '25215.i', 'p': 43, 'prec': 20, 'unit': 4964161508777525277612412934238, 'val': 1}
  • id: 1200616
    {'lmfdb_iso': '25215.i', 'p': 47, 'prec': 20, 'unit': 1235073491781361094194741596141, 'val': 1}
  • id: 1200612
    {'lmfdb_iso': '25215.i', 'p': 53, 'prec': 20, 'unit': 297209335081954504776187823953070, 'val': 1}
  • id: 1200613
    {'lmfdb_iso': '25215.i', 'p': 59, 'prec': 20, 'unit': 491444153541656409197888651869912, 'val': 1}
  • id: 1200617
    {'lmfdb_iso': '25215.i', 'p': 61, 'prec': 20, 'unit': 1706902657718771484212259536320831, 'val': 1}
  • id: 1200602
    {'lmfdb_iso': '25215.i', 'p': 67, 'prec': 20, 'unit': 8290829484022710164379851135965484, 'val': 1}
  • id: 1200615
    {'lmfdb_iso': '25215.i', 'p': 71, 'prec': 20, 'unit': 87387005903773498328800552757444766, 'val': 1}
  • id: 1200605
    {'lmfdb_iso': '25215.i', 'p': 73, 'prec': 20, 'unit': 89284995630393733762814672797038568, 'val': 1}
  • id: 1200609
    {'lmfdb_iso': '25215.i', 'p': 79, 'prec': 20, 'unit': 1045805081070345407744459142988784967, 'val': 1}
  • id: 1200611
    {'lmfdb_iso': '25215.i', 'p': 83, 'prec': 20, 'unit': 583939690021832880676863210416200796, 'val': 1}
  • id: 1200614
    {'lmfdb_iso': '25215.i', 'p': 89, 'prec': 20, 'unit': 1686088912146319442306734900063125064, 'val': 1}
  • id: 1200601
    {'lmfdb_iso': '25215.i', 'p': 97, 'prec': 20, 'unit': 13459760722252530677985525359618242271, 'val': 1}