{
  "id": 3135,
  "curve_key": "64225451427964951824696260930615880084961:-16276489694097156559615009404883552247007327609458794766057041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1338030238082603163014505436054497501770",
    "18838529738538375647591054661737968540822087057943137668900"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 281.88965459577054,
  "faltings_height": 20.924502980800938,
  "conductor": "14957195101499347727901912655348880567251830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "43",
    "71",
    "103",
    "151",
    "797",
    "94253",
    "253424587069203922319"
  ],
  "discriminant": "513083891855401048192109684639722035745091861022437955616593459862597668421659939362812544692356596284631040000",
  "regulator": "7674389289586.16487771178770341448355826763434083093900741565",
  "points": [
    [
      "24262392069982068340",
      "25634044426632283614183209830"
    ],
    [
      "1034936550973860953140/49",
      "-5699165676049384182391171670/343"
    ],
    [
      "21481178271245279470",
      "-2891448187328691878503439720"
    ],
    [
      "52848766841115555074272/2401",
      "-841361155887056401969615521224666/117649"
    ],
    [
      "235255174478782127023540/10201",
      "-16176992322851677525888526027798770/1030301"
    ],
    [
      "11172312903670604345920/529",
      "19453998675281668323292211030/12167"
    ],
    [
      "21547627698974103610",
      "-3423660275451050517742153190"
    ],
    [
      "21203263576034947752",
      "-671528149552281842876219214"
    ],
    [
      "784278431849658206056/25",
      "10994920297321104154545254568206/125"
    ],
    [
      "21121245430551532780",
      "-17381267277437713138736570"
    ],
    [
      "110326051389368741146690/529",
      "-36115779741719952775776442982298730/12167"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-006, rational kernel x=-10559122671197498060. Source: https://dujella.github.io/tors/z4old9101112.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:38:54",
  "updated_at": "2026-09-26 20:38:54"
}