{
  "id": 3023,
  "curve_key": "12745254359213429072361713701456:-45485049225378662072673759221137646778534839104",
  "ainvs": [
    "0",
    "1",
    "0",
    "-265526132483613105674202368780",
    "52644732899743733334661578634911125703996100"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 214.8681353550571,
  "faltings_height": 15.642602214954449,
  "conductor": "28662861085935403583774269180",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "17",
    "19",
    "31",
    "61",
    "71",
    "79",
    "163",
    "241",
    "661",
    "1129",
    "99787"
  ],
  "discriminant": "849909490292105154064329155897592193270016727909570744403301820138055808582644047968000",
  "regulator": "16531353.2605234007791993764344309609858582214625929165",
  "points": [
    [
      "24597240001299064/81",
      "-90699937635940342025030/729"
    ],
    [
      "831611369121431712/1369",
      "-544383732893313377039066102/50653"
    ],
    [
      "83341752902352120",
      "-24059448296789515209529930"
    ],
    [
      "49166047684317300/169",
      "308242719378230664194530/2197"
    ],
    [
      "891132505099406845/2916",
      "-31634601015903294349928845/157464"
    ],
    [
      "1089640996179725/4",
      "5810522996380455405195/8"
    ],
    [
      "8537431420963546614040/46280809",
      "992669087871520036795292590848590/314848343627"
    ],
    [
      "49946708578273738264/189225",
      "80151436342686309253228984562/82312875"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-059, rational kernel x=-146458586456760. Source: https://dujella.github.io/tors/z6old678.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 20:33:44",
  "updated_at": "2026-09-26 20:33:44"
}