Elliptic curve data - 75810.q4

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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': '75810x', 'Clabel': '75810x4', 'Cnumber': 4, 'abc_quality': 1.0358020223701003, 'absD': 5670478558097362800, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 63840, 'ainvs': [1, 1, 0, -5440277, -4884968259], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 75810, 'degree': 3538944, 'elladic_images': ['16.48.0.96'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5735017259188379675403198419', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [378499465220294881, 120530818800], 'lmfdb_iso': '75810.q', 'lmfdb_label': '75810.q4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -15070, 710612], 'min_quad_twist_disc': -19, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0.v.1', '28.12.0.h.1', '56.48.0.bl.2', '76.12.0.?', '80.96.2.?', '96.96.1.?', '112.96.1.?', '152.48.0.?', '304.96.0.?', '480.192.5.?', '532.24.0.?', '560.192.5.?', '672.192.5.?', '1064.96.0.?', '1520.192.2.?', '1824.192.1.?', '2128.192.1.?', '3360.384.13.?', '9120.384.5.?', '10640.384.5.?', '12768.384.5.?', '63840.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.3994223215477309040387906703', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2527], [3, 4, 25270], [5, 6, 15162], [7, 8, 10830], [19, 182, 210]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1012822363356177375358061260', 'prec': 100}, 'szpiro_ratio': 5.174590603250028, '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, -1, -1, 1, -1, -4, -1, 2, 1, -1, 1, 2, -1, 0, 1], 'aplist': [-1, -1, 1, -1, -4, 2, 2, 0, -8, 2, 0, -6, 6, -4, 0, 10, -12, 14, 12, 8, 10, -16, -12, -10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 75810, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '75810.q', 'trace_hash': 2119838942422431444}
• 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': '0.0058168089857457815154623382521', 'prec': 110}, 'conductor': 75810, 'gens': [[13397, 1518734, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.3994223215477309040387906703', 'prec': 100}], 'lmfdb_label': '75810.q4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.098855899147888571469323272886', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4792707946231383388222807762475662548', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-5461, 5461, 2]], 'xcoord_integral_points': [13397]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': [3, 0], '5': [2, 0], '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': 'a', '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '75810.q4'}
• ec_torsion_growth •

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

  
  
  • id: 3583890
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 2]}
  • id: 3583892
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '75810.q4', 'torsion': [8]}
  • id: 3583891
    {'degree': 2, 'field': [133, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [4]}
  • id: 3583893
    {'degree': 4, 'field': [137, 4, -3, -2, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 8]}
  • id: 3583894
    {'degree': 4, 'field': [215, 10, -9, -2, 1], 'lmfdb_label': '75810.q4', 'torsion': [16]}
  • id: 3583895
    {'degree': 4, 'field': [5555, 130, -129, -2, 1], 'lmfdb_label': '75810.q4', 'torsion': [16]}
  • id: 3583899
    {'degree': 8, 'field': [-490880, 366280, -95945, 14634, -3273, 324, 1, -2, 1], 'lmfdb_label': '75810.q4', 'torsion': [6]}
  • id: 3583896
    {'degree': 8, 'field': [4281, 31220, -4084, -840, -163, -140, -26, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 4]}
  • id: 3583898
    {'degree': 8, 'field': [40289, -12304, 13254, -1852, 807, 140, -42, -4, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 16]}
  • id: 3583897
    {'degree': 8, 'field': [1125721, 0, 132164, 0, 3566, 0, -76, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [8]}
  • id: 3583901
    {'degree': 16, 'field': [95481, 0, 432220, 0, 364450, 0, 146780, 0, 38723, 0, 6500, 0, 674, 0, 40, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 16]}
  • id: 3583906
    {'degree': 16, 'field': [4202500, 0, -3320125, 0, -345950, 0, 691469, 0, 119587, 0, 5609, 0, 571, 0, 38, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [24]}
  • id: 3583900
    {'degree': 16, 'field': [666930625, 0, -415575000, 0, 102658650, 0, 2927700, 0, 562411, 0, -11916, 0, -114, 0, -36, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [4, 8]}
  • id: 3583902
    {'degree': 16, 'field': [93019962775, 32332770800, -28922824100, -6718855000, 3112059200, 282491000, -71097480, -18091000, 2476661, 1281112, -174972, -42176, 5270, 784, -92, -8, 1], 'lmfdb_label': '75810.q4', 'torsion': [32]}
  • id: 3583904
    {'degree': 16, 'field': [103569269136, -75085994880, 160850968816, -100716488320, 22886395264, -3841943616, 463572768, -2780904, 581304, 230832, -221604, 29988, -6735, 840, -50, -4, 1], 'lmfdb_label': '75810.q4', 'torsion': [2, 6]}
  • id: 3583905
    {'degree': 16, 'field': [1361851656256, 0, 396050488421, 0, 39679197754, 0, 2281217883, 0, 85341291, 0, 2063103, 0, 30919, 0, 266, 0, 1], 'lmfdb_label': '75810.q4', 'torsion': [12]}
  • id: 3583903
    {'degree': 16, 'field': [371262133960225, 40263275628200, -38121888509700, -4216521041600, 1943904953550, 193665557400, -58666829480, -4953839000, 1122646911, 75903512, -13883072, -698376, 108570, 3584, -492, -8, 1], 'lmfdb_label': '75810.q4', 'torsion': [32]}
• 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: 1842451
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '75810.q4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1842452
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '75810.q4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1842453
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '75810.q4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1842454
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '75810.q4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1842455
    {'conductor': 75810, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '75810.q4', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2164934
    {'adelic_gens': [[4352, 53789, 37867, 19362], [1, 0, 32, 1], [21281, 57152, 17936, 20673], [57362, 19, 7695, 22478], [35721, 57152, 21964, 46589], [43679, 0, 0, 63839], [63809, 32, 63808, 33], [5, 28, 68, 381], [16151, 50426, 12198, 875], [23, 18, 61278, 61835], [1, 32, 0, 1]], 'adelic_image': '63840.768.13.?', 'conductor': 75810, 'lmfdb_label': '75810.q4', 'prime': 0}
  • id: 313151
    {'conductor': 75810, 'elladic_image': '16.48.0.96', 'lmfdb_label': '75810.q4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3901370
    {'lmfdb_iso': '75810.q', 'p': 11, 'prec': 20, 'unit': 3625914029074650155, 'val': 2}
  • id: 3901376
    {'lmfdb_iso': '75810.q', 'p': 13, 'prec': 20, 'unit': 434500375278755824421, 'val': 1}
  • id: 3901378
    {'lmfdb_iso': '75810.q', 'p': 17, 'prec': 20, 'unit': 121561843433267652478215, 'val': 1}
  • id: 3901382
    {'lmfdb_iso': '75810.q', 'p': 23, 'prec': 20, 'unit': 51596064816197355061921579, 'val': 1}
  • id: 3901375
    {'lmfdb_iso': '75810.q', 'p': 29, 'prec': 20, 'unit': 3644447561594741715241584596, 'val': 1}
  • id: 3901371
    {'lmfdb_iso': '75810.q', 'p': 37, 'prec': 20, 'unit': 544502796416722760234263002946, 'val': 1}
  • id: 3901373
    {'lmfdb_iso': '75810.q', 'p': 41, 'prec': 20, 'unit': 68856763717732192563890739828, 'val': 1}
  • id: 3901374
    {'lmfdb_iso': '75810.q', 'p': 43, 'prec': 20, 'unit': 9049286508950845986323395223058, 'val': 1}
  • id: 3901380
    {'lmfdb_iso': '75810.q', 'p': 53, 'prec': 20, 'unit': 121157745602304596917057464763632, 'val': 1}
  • id: 3901384
    {'lmfdb_iso': '75810.q', 'p': 59, 'prec': 20, 'unit': 611692093923823607856267901024409, 'val': 1}
  • id: 3901385
    {'lmfdb_iso': '75810.q', 'p': 61, 'prec': 20, 'unit': 6869462399163967249803423022644382, 'val': 1}
  • id: 3901369
    {'lmfdb_iso': '75810.q', 'p': 67, 'prec': 20, 'unit': 27026913920249937949826353004124826, 'val': 1}
  • id: 3901372
    {'lmfdb_iso': '75810.q', 'p': 71, 'prec': 20, 'unit': 147811739340842927686750736753085216, 'val': 1}
  • id: 3901381
    {'lmfdb_iso': '75810.q', 'p': 73, 'prec': 20, 'unit': 3936708343526089293975098299563723, 'val': 1}
  • id: 3901377
    {'lmfdb_iso': '75810.q', 'p': 79, 'prec': 20, 'unit': 635118739471023128242140174608532055, 'val': 1}
  • id: 3901379
    {'lmfdb_iso': '75810.q', 'p': 83, 'prec': 20, 'unit': 1082881136174404136197210342438976043, 'val': 1}
  • id: 3901383
    {'lmfdb_iso': '75810.q', 'p': 89, 'prec': 20, 'unit': 10124267442112097030201929707537275784, 'val': 1}
  • id: 3901368
    {'lmfdb_iso': '75810.q', 'p': 97, 'prec': 20, 'unit': 8770154765285897492432119478137094329, 'val': 1}