{
  "id": 3013,
  "curve_key": "472251388969359959707014502612127041:-112486333908741076782392247893818174793124572802632161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-9838570603528332493896135471085980",
    "130192516098079949159739773657150735222919929264400"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 246.428458549064,
  "faltings_height": 18.596208802899575,
  "conductor": "1778372045405097567630514914990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "43",
    "47",
    "71",
    "127",
    "191",
    "239",
    "359",
    "1223",
    "5881",
    "15583"
  ],
  "discriminant": "53627881079994132777818047919012861197732643143663563850076779341830589978361477982298875528477184000000",
  "regulator": "87300900.4056206373622225057964331284695448897811261185",
  "points": [
    [
      "-27704998359007890",
      "-19532144207274497684660430"
    ],
    [
      "91962779652885960",
      "-1775809393498642586499180"
    ],
    [
      "-13043679945785640",
      "-16009511602178088065673180"
    ],
    [
      "79709536522896745272",
      "-711647764880967953005226198364"
    ],
    [
      "133162924839344481818190/326041",
      "-47186175712246858147150599647299680/186169411"
    ],
    [
      "89649709477742633352/961",
      "-146624548933986115178632674084/29791"
    ],
    [
      "9314642436058095580760/1681",
      "-898834754570075044134250780874780/68921"
    ],
    [
      "56119614469952386461550230313584993806863494975729845712/4185254789639178937591551350782941578881",
      "-223128374124914590114424379851524074640966368171815315210488124056152780800134841868/270758969877756342231168104328857519276414071693019244625471"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-073, rational kernel x=52620481624914360. 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 20:33:18",
  "updated_at": "2026-09-26 20:33:18"
}