Elliptic curve data - 57798.bm2

Formats: - HTML - YAML - JSON - 2025-10-10T03:21:32.715935

• 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': '57798bf', 'Clabel': '57798bf4', 'Cnumber': 4, 'abc_quality': 1.0101536552434738, 'absD': 2979763204490971938, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5928, 'ainvs': [1, -1, 1, -635810, 212234195], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 57798, 'degree': 1244160, 'elladic_images': ['8.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2838564592948986195583099693', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 38, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-8078253774625, 846825858], 'lmfdb_iso': '57798.bm', 'lmfdb_label': '57798.bm2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -418, -3610], 'min_quad_twist_disc': -39, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.a.1', '24.24.0.p.1', '39.8.0-3.a.1.1', '78.24.0.?', '228.24.0.?', '312.48.0.?', '456.48.1.?', '2964.48.0.?', '5928.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.415780127245289206756142899', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1521], [3, 8, 338], [13, 86, 342], [19, 20, 3042]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.45207563623007540583394363005', 'prec': 103}, 'szpiro_ratio': 4.730453564886606, '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, 0, 1, 0, 0, 4, 1, 0, 0, 0, 0, 0, 4, 0, 1, -6, 0, -1, 0], 'aplist': [1, 0, 0, 4, 0, 0, -6, -1, 6, -6, -2, 4, 6, -4, 6, -6, -12, 14, -8, 0, -14, -10, -12, -6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 57798, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '57798.bm', 'trace_hash': 314875260649831383}
• 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': '0.010381676325299806226146568351', 'prec': 107}, 'conductor': 57798, 'gens': [[443709, 231656387, 20]], 'heights': [{'__RealLiteral__': 0, 'data': '11.415780127245289206756142899', 'prec': 100}], 'lmfdb_label': '57798.bm2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.24707352106195494117674708454', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.282147966830342484986789819545649276', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-3717, 3713, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': 'a', '5': [1, 5, 0], '7': [1, 0], '11': [1, 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': '57798.bm2'}
• ec_torsion_growth •

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

  
  
  • id: 2783562
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '57798.bm2', 'torsion': [6]}
  • id: 2783561
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 2]}
  • id: 2783563
    {'degree': 4, 'field': [-1352, 0, 65, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [4]}
  • id: 2783564
    {'degree': 4, 'field': [27, 2, -1, -2, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 6]}
  • id: 2783565
    {'degree': 6, 'field': [768, 0, 0, -54, 0, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [6]}
  • id: 2783568
    {'degree': 8, 'field': [157, 778, -740, -74, 33, 2, 4, -4, 1], 'lmfdb_label': '57798.bm2', 'torsion': [12]}
  • id: 2783567
    {'degree': 8, 'field': [11664, 0, -8640, 0, 1530, 0, 24, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 4]}
  • id: 2783566
    {'degree': 8, 'field': [21316, 0, 67500, 0, 773, 0, -36, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 4]}
  • id: 2783569
    {'degree': 12, 'field': [2721, -8001, 8145, -1218, -1953, 729, -200, 177, 87, -16, 15, -3, 1], 'lmfdb_label': '57798.bm2', 'torsion': [3, 6]}
  • id: 2783570
    {'degree': 12, 'field': [600928, 502848, 127344, -76032, -28344, 2592, 4612, 0, 60, -108, 12, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 6]}
  • id: 2783573
    {'degree': 16, 'field': [1819827, -540432, 1041444, -1030968, 596856, -119160, 65152, -3224, -17427, 4712, 5948, -3072, -34, 224, -12, -8, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 12]}
  • id: 2783572
    {'degree': 16, 'field': [4939321, -1405252, 1832692, -839236, 421490, -115408, 222468, -149020, 27587, 4480, 1260, -1436, 482, -140, 40, -8, 1], 'lmfdb_label': '57798.bm2', 'torsion': [2, 12]}
  • id: 2783571
    {'degree': 16, 'field': [108383174656, 0, -54113501184, 0, -5779928192, 0, 69466272, 0, 4108830, 0, 274548, 0, 4015, 0, -162, 0, 1], 'lmfdb_label': '57798.bm2', 'torsion': [8]}
  • id: 2783574
    {'degree': 18, 'field': [-206953977, -120539916, 375469308, 260437197, -213385977, -162596466, 63478976, 50064753, -11401770, -8434501, 1341231, 792105, -100191, -39351, 4443, 958, -105, -9, 1], 'lmfdb_label': '57798.bm2', 'torsion': [18]}
• 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: 1390691
    {'conductor': 57798, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57798.bm2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1390692
    {'conductor': 57798, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57798.bm2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1390693
    {'conductor': 57798, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '57798.bm2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1390694
    {'conductor': 57798, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '57798.bm2', 'prime': 19, 'reduction_type': -1, '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: 2047711
    {'adelic_gens': [[1834, 4563, 3393, 4096], [5471, 0, 0, 5927], [11, 2, 5878, 5919], [5682, 5161, 2717, 1730], [1, 0, 12, 1], [1, 6, 6, 37], [3745, 468, 1950, 2809], [5917, 12, 5916, 13], [1975, 5460, 1742, 3119], [1, 12, 0, 1]], 'adelic_image': '5928.96.1.?', 'conductor': 57798, 'lmfdb_label': '57798.bm2', 'prime': 0}
  • id: 245270
    {'conductor': 57798, 'elladic_image': '8.6.0.5', 'lmfdb_label': '57798.bm2', 'modell_image': '2B', 'prime': 2}
  • id: 245271
    {'conductor': 57798, 'elladic_image': '3.4.0.1', 'lmfdb_label': '57798.bm2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2929605
    {'lmfdb_iso': '57798.bm', 'p': 7, 'prec': 20, 'unit': 10380014385631972, 'val': 1}
  • id: 2929610
    {'lmfdb_iso': '57798.bm', 'p': 17, 'prec': 20, 'unit': 146106558934916164770033, 'val': 1}
  • id: 2929615
    {'lmfdb_iso': '57798.bm', 'p': 23, 'prec': 20, 'unit': 54062848398450337672032349, 'val': 1}
  • id: 2929608
    {'lmfdb_iso': '57798.bm', 'p': 29, 'prec': 20, 'unit': 1453256834411294052037058536, 'val': 1}
  • id: 2929619
    {'lmfdb_iso': '57798.bm', 'p': 31, 'prec': 20, 'unit': 12659806224479714666352039037, 'val': 1}
  • id: 2929604
    {'lmfdb_iso': '57798.bm', 'p': 37, 'prec': 20, 'unit': 36075467563332734685518067810, 'val': 1}
  • id: 2929606
    {'lmfdb_iso': '57798.bm', 'p': 41, 'prec': 20, 'unit': 2013792567505001572199048187312, 'val': 1}
  • id: 2929607
    {'lmfdb_iso': '57798.bm', 'p': 43, 'prec': 20, 'unit': 6502268094395307075098112033030, 'val': 1}
  • id: 2929617
    {'lmfdb_iso': '57798.bm', 'p': 47, 'prec': 20, 'unit': 36058122755110918539628289250094, 'val': 1}
  • id: 2929612
    {'lmfdb_iso': '57798.bm', 'p': 53, 'prec': 20, 'unit': 406069612661146636284905052979373, 'val': 1}
  • id: 2929613
    {'lmfdb_iso': '57798.bm', 'p': 59, 'prec': 20, 'unit': 79862019698986758771895291745018, 'val': 1}
  • id: 2929618
    {'lmfdb_iso': '57798.bm', 'p': 61, 'prec': 20, 'unit': 762392759055449458655222700858068, 'val': 1}
  • id: 2929603
    {'lmfdb_iso': '57798.bm', 'p': 67, 'prec': 20, 'unit': 41506277718973470884508741166111446, 'val': 1}
  • id: 2929614
    {'lmfdb_iso': '57798.bm', 'p': 73, 'prec': 20, 'unit': 95593309838645264841734761900998631, 'val': 1}
  • id: 2929609
    {'lmfdb_iso': '57798.bm', 'p': 79, 'prec': 20, 'unit': 679903050210406053106003589632772342, 'val': 1}
  • id: 2929611
    {'lmfdb_iso': '57798.bm', 'p': 83, 'prec': 20, 'unit': 85457339331053714433388065909321203, 'val': 1}
  • id: 2929616
    {'lmfdb_iso': '57798.bm', 'p': 89, 'prec': 20, 'unit': 9881869841627440087567639945451363266, 'val': 1}
  • id: 2929602
    {'lmfdb_iso': '57798.bm', 'p': 97, 'prec': 20, 'unit': 22493151338744734409387074646673990521, 'val': 1}