{
  "id": 3007,
  "curve_key": "21754160598603309681621275583048016:-3208808260914642193853148597375878868814359275040064",
  "ainvs": [
    "0",
    "1",
    "0",
    "-453211679137568951700443241313500",
    "3713898450132687573296510423328727753572576130500"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 237.1954787052456,
  "faltings_height": 17.450755854990216,
  "conductor": "31602563084617300276824095632860",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "29",
    "37",
    "79",
    "109",
    "127",
    "233",
    "3613",
    "6659",
    "3477917"
  ],
  "discriminant": "-830602544155307664850951325201755525925566735828168023724591178422279297005169796990220008352000",
  "regulator": "137327222.931258973503496267399845810787590304332957667",
  "points": [
    [
      "35452259606936709960/4489",
      "238193593758753171102863068770/300763"
    ],
    [
      "-8585345847341832",
      "2640467266171239089668566"
    ],
    [
      "4703760766360005/4",
      "14271817830641558564049585/8"
    ],
    [
      "334628002978089624621585/190329616",
      "4488882382278792034513521246714431265/2625787382336"
    ],
    [
      "3750150901875524664/361",
      "2443195879252480573795546830/6859"
    ],
    [
      "7988290170020340",
      "-776702678417372813228010"
    ],
    [
      "42753070067260678892092320/3362956081",
      "-16195368564402253131898630635863309730/195021186093271"
    ],
    [
      "-10246256009443329957323721430893/629914473021409",
      "-41172238598535378072199672013679906426949737822/15809654545595206158673"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-027, rational kernel x=12291171619722000. 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 20:33:02",
  "updated_at": "2026-09-26 20:33:02"
}