Elliptic curve data - 6825.h2

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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': '6825b', 'Clabel': '6825b2', 'Cnumber': 2, 'abc_quality': 0.9665140132672618, 'absD': 5661904081640625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5460, 'ainvs': [1, 1, 0, -46650, 1371375], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6825, 'degree': 41472, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7153323419430367042996181387', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2], 'jinv': [718576775407009, 362361861225], 'lmfdb_iso': '6825.h', 'lmfdb_label': '6825.h2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1866, 10971], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0-2.a.1.1', '140.12.0.?', '260.12.0.?', '364.12.0.?', '420.24.0.?', '780.24.0.?', '1092.24.0.?', '1820.24.0.?', '5460.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 325], [5, 18, 273], [7, 8, 975], [13, 14, 525]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.91061338572598651699923847209', 'prec': 103}, 'szpiro_ratio': 4.96864453386851, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, -1, -1, -3, 1, 0, -4, 1, 1, -1, 0, -1, -2, 1, 0, 0], 'aplist': [1, -1, 0, -1, -4, 1, -2, 0, 0, -10, -4, -10, 6, 8, -4, 10, -12, -10, 4, 0, -6, 0, 16, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 6825, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6825.h', 'trace_hash': 2153551769461126472}
• 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': '0.032365420848022027901829697896', 'prec': 107}, 'conductor': 6825, 'gens': [], 'heights': [], 'lmfdb_label': '6825.h2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37796428550041924240834603882', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.75592857100083848481669207763825924846', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-230, 115, 1], [30, -15, 1]], 'xcoord_integral_points': [-230, 30]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [0, 0], '5': 'a', '7': [0, 0], '13': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '6825.h2'}
• ec_torsion_growth •

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

  
  
  • id: 358573
    {'degree': 4, 'field': [64, 0, -19, 0, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 4]}
  • id: 358572
    {'degree': 4, 'field': [256, 16, 17, -1, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 4]}
  • id: 358574
    {'degree': 4, 'field': [1521, 0, -13, 0, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 4]}
  • id: 358575
    {'degree': 8, 'field': [-169, 169, -208, 77, -35, -7, 7, -4, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 6]}
  • id: 358578
    {'degree': 16, 'field': [19307236, 0, -222696708, 0, 407360473, 0, -197286336, 0, -733560, 0, 281004, 0, 148, 0, -108, 0, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 8]}
  • id: 358576
    {'degree': 16, 'field': [38950081, 0, -9642345, 0, 339977, 0, -693990, 0, 124518, 0, 8010, 0, -103, 0, 15, 0, 1], 'lmfdb_label': '6825.h2', 'torsion': [4, 4]}
  • id: 358579
    {'degree': 16, 'field': [99272525, -16000420, -91242056, -132626256, 151652179, -40546688, 29251306, -391288, 1663440, 466448, -45220, 11284, -1141, -84, 74, -4, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 8]}
  • id: 358577
    {'degree': 16, 'field': [103887091, -282676614, 209023293, -7857378, -15899033, -4764252, 3318132, -77484, -426600, 91392, 14316, -5868, 613, 138, 15, -6, 1], 'lmfdb_label': '6825.h2', 'torsion': [2, 8]}
• 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: 139107
    {'conductor': 6825, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6825.h2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 139108
    {'conductor': 6825, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '6825.h2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 139109
    {'conductor': 6825, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6825.h2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 139110
    {'conductor': 6825, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6825.h2', 'prime': 13, '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: 1709098
    {'adelic_gens': [[1, 0, 4, 1], [1089, 5458, 1094, 1], [1, 4, 0, 1], [3, 2, 3638, 5459], [2341, 4, 4682, 9], [5457, 4, 5456, 5], [4201, 2, 0, 1], [2731, 4, 0, 1]], 'adelic_image': '5460.48.0.?', 'conductor': 6825, 'lmfdb_label': '6825.h2', 'prime': 0}
  • id: 33742
    {'conductor': 6825, 'elladic_image': '2.6.0.1', 'lmfdb_label': '6825.h2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 6825.h does not appear in ec_padic