{
  "id": 3142,
  "curve_key": "29539743470147149622557861681308041320321:-4785453407105906373005997910960835798787732155191516988930881",
  "ainvs": [
    "1",
    "0",
    "0",
    "-615411322294732283803288785027250860840",
    "5538719221187391635372324416383813743465156669756429313600"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 279.5596656590436,
  "faltings_height": 21.2428941676319,
  "conductor": "31000471439531693917957022221199714058221545530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "67",
    "71",
    "73",
    "103",
    "127",
    "293",
    "1091",
    "682327",
    "102838432973"
  ],
  "discriminant": "1664184493908733386068254585085809176300454477056389508312508481164956558156678807087667633912450105451479449600000000",
  "regulator": "3299878871.07795810827014301302224954130762275056448073487855",
  "points": [
    [
      "34671110493770918750004/1849",
      "1934676178040911990365369070753164/79507"
    ],
    [
      "-21305867139566753520",
      "94757618715859900542658542360"
    ],
    [
      "-140823980180769576788580/6889",
      "55955830766308882932242116542440820/571787"
    ],
    [
      "-319982428856419447650208320/32615521",
      "19206374758511903734988452128233827541160/186267240431"
    ],
    [
      "-4565286891241286448",
      "90846571013826078600309586776"
    ],
    [
      "434851104684132361680",
      "-9053524518644420246943534089640"
    ],
    [
      "-448387402951542959379120/22801",
      "344913413265498395233597595965526760/3442951"
    ],
    [
      "-2148837525085444110975120/96721",
      "2731382068027181875632023524190237160/30080231"
    ],
    [
      "4536129681809404980",
      "53296071177645173186531232360"
    ],
    [
      "4008824717924459681136/841",
      "1270459687338992356169640908016408/24389"
    ],
    [
      "1042262140963440593822928/26569",
      "-885050863905891924581801888926869816/4330747"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-042, rational kernel x=-136324006169006490241/4. Source: https://dujella.github.io/tors/z2z2old1011121314.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 20:39:16",
  "updated_at": "2026-09-26 20:39:16"
}