{
  "id": 3010,
  "curve_key": "1230204340602549589842614328603947041:-1364475941443229553107904707847224274684315025612874161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-25629257095886449788387798512582230",
    "1579254561855589758405784950165972094815270292484900"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 249.30073090182898,
  "faltings_height": 18.045609179084614,
  "conductor": "152125511168293484465581800363930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "29",
    "31",
    "73",
    "139",
    "167",
    "227",
    "251",
    "499",
    "2093890919"
  ],
  "discriminant": "109088779417669092878744295651414949219750559446567665337018377719787528386054123318795712000",
  "regulator": "415273884.484392561728754381669849886881962947182633557",
  "points": [
    [
      "155388413688971783516/1681",
      "-336311789269181201837073638/68921"
    ],
    [
      "92459587550434982",
      "-16205560242171352921474"
    ],
    [
      "157355170324156420",
      "37981241156453790338792770"
    ],
    [
      "256273178549112340220/1681",
      "2402654841631484192673797290810/68921"
    ],
    [
      "37457614190233003683278120/405257161",
      "1856937715316597898332265677467070/8158231908091"
    ],
    [
      "6517855317671712108739009095775/70555732864516",
      "15600775153640319672872282126549450601675145/592650234905786812936"
    ],
    [
      "161401710795746036",
      "40586276713985948541717242"
    ],
    [
      "216679494873321769879700/2343961",
      "24153180046901876908066510085870/3588604291"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-013, rational kernel x=-46214398621289140. 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 20:33:10",
  "updated_at": "2026-09-26 20:33:10"
}