Elliptic curve data - 3075.g1

Formats: - HTML - YAML - JSON - 2025-11-10T02:43:14.266065

• 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': '3075m', 'Clabel': '3075m1', 'Cnumber': 1, 'abc_quality': 1.0113100029644233, 'absD': 28366875, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 6, 'ainvs': [0, 1, 1, -3483, 77969], 'analytic_rank': 1, 'bad_primes': [3, 5, 41], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 3075, 'degree': 1512, 'elladic_images': ['3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.61768564220526634975567354559', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 3], 'jinv': [-7478746316800, 45387], 'lmfdb_iso': '3075.g', 'lmfdb_label': '3075.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -3483, 77969], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '6.16.0-6.b.1.2'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.87156197878034665693519608732', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 1025], [5, 14, 123], [41, 42, 75]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.081206338060566224888753767848', 'prec': 107}, 'szpiro_ratio': 4.49266318717151, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 0, 1, -2, 0, 0, -1, 0, 1, 0, 0, -2, -1, 0, 0, 4, 0, 0, -7, 0], 'aplist': [0, 1, 0, -1, 0, -1, 0, -7, 6, 6, 5, 2, -1, -7, -12, -6, -12, -13, -13, 12, 2, 8, 12, -12, -1], 'class_deg': 3, 'class_size': 2, 'conductor': 3075, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '3075.g', 'trace_hash': 222030762975357796}
• 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': '0.29072679999815606071986700171', 'prec': 103}, 'conductor': 3075, 'gens': [[-57, 307, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.87156197878034665693519608732', 'prec': 103}], 'lmfdb_label': '3075.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8713043269616949478194693797', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2619154042139193092141385937085030851', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [[33, 7, 1]], 'xcoord_integral_points': [-57, 33, 213]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': [2, 0], '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 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': '3075.g1'}
• ec_torsion_growth •

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

  
  
  • id: 159334
    {'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '3075.g1', 'torsion': [6]}
  • id: 159335
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '3075.g1', 'torsion': [2, 6]}
  • id: 159336
    {'degree': 6, 'field': [38988, 0, -683, 0, 1, 0, 1], 'lmfdb_label': '3075.g1', 'torsion': [3, 3]}
  • id: 159337
    {'degree': 9, 'field': [-20237, -41412, -12636, 728, 471, 498, 86, -45, -3, 1], 'lmfdb_label': '3075.g1', 'torsion': [9]}
  • id: 159338
    {'degree': 12, 'field': [-8586, 10476, -9648, 6948, -5982, 3960, -2424, 912, -296, 50, 6, -4, 1], 'lmfdb_label': '3075.g1', 'torsion': [12]}
  • id: 159339
    {'degree': 18, 'field': [7077888, 0, 0, 0, 0, 0, 1727632, 0, 0, 0, 0, 0, -1064, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3075.g1', 'torsion': [6, 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: 55055
    {'conductor': 3075, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '3075.g1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 55056
    {'conductor': 3075, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '3075.g1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 55057
    {'conductor': 3075, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3075.g1', 'prime': 41, '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: 1683934
    {'adelic_gens': [[0, 1, 1, 0], [4, 3, 3, 1], [3, 4, 2, 5]], 'adelic_image': '6.16.0.?', 'conductor': 3075, 'lmfdb_label': '3075.g1', 'prime': 0}
  • id: 15313
    {'conductor': 3075, 'elladic_image': '3.8.0.1', 'lmfdb_label': '3075.g1', 'modell_image': '3B.1.1', 'prime': 3}
• ec_padic •

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

  
  
  • id: 100177
    {'lmfdb_iso': '3075.g', 'p': 7, 'prec': 20, 'unit': 1235546564523407, 'val': 1}
  • id: 100181
    {'lmfdb_iso': '3075.g', 'p': 13, 'prec': 20, 'unit': 12882004456915353641, 'val': 1}
  • id: 100184
    {'lmfdb_iso': '3075.g', 'p': 19, 'prec': 20, 'unit': 217688918957620673013721, 'val': 1}
  • id: 100186
    {'lmfdb_iso': '3075.g', 'p': 23, 'prec': 20, 'unit': 17584724198450356914587771, 'val': 1}
  • id: 100180
    {'lmfdb_iso': '3075.g', 'p': 29, 'prec': 20, 'unit': 2404221921647983033103635351, 'val': 1}
  • id: 100191
    {'lmfdb_iso': '3075.g', 'p': 31, 'prec': 20, 'unit': 9901589509481193606641317155, 'val': 1}
  • id: 100176
    {'lmfdb_iso': '3075.g', 'p': 37, 'prec': 20, 'unit': 235786904169456069024431872903, 'val': 1}
  • id: 100179
    {'lmfdb_iso': '3075.g', 'p': 43, 'prec': 20, 'unit': 1594468489893900114807228758783, 'val': 1}
  • id: 100189
    {'lmfdb_iso': '3075.g', 'p': 47, 'prec': 20, 'unit': 14670020546081002125497996574793, 'val': 1}
  • id: 100185
    {'lmfdb_iso': '3075.g', 'p': 53, 'prec': 20, 'unit': 283953936228876387002440391281808, 'val': 1}
  • id: 100183
    {'lmfdb_iso': '3075.g', 'p': 59, 'prec': 20, 'unit': 1744434915634618000350500551783674, 'val': 1}
  • id: 100190
    {'lmfdb_iso': '3075.g', 'p': 61, 'prec': 20, 'unit': 2992494368648992902386756486327587, 'val': 1}
  • id: 100175
    {'lmfdb_iso': '3075.g', 'p': 67, 'prec': 20, 'unit': 37441559333337932776056169673425554, 'val': 1}
  • id: 100188
    {'lmfdb_iso': '3075.g', 'p': 71, 'prec': 20, 'unit': 104653712698762311470809822433807381, 'val': 1}
  • id: 100178
    {'lmfdb_iso': '3075.g', 'p': 73, 'prec': 20, 'unit': 229138508283820151548872919791995298, 'val': 1}
  • id: 100182
    {'lmfdb_iso': '3075.g', 'p': 79, 'prec': 20, 'unit': 647894963512387446451089395008248086, 'val': 1}
  • id: 100174
    {'lmfdb_iso': '3075.g', 'p': 83, 'prec': 20, 'unit': 2157483649598511221520857401362420603, 'val': 1}
  • id: 100187
    {'lmfdb_iso': '3075.g', 'p': 89, 'prec': 20, 'unit': 7404164085588605552172255504086056869, 'val': 1}
  • id: 100173
    {'lmfdb_iso': '3075.g', 'p': 97, 'prec': 20, 'unit': 9188762178535153641570572930666423588, 'val': 1}