{
  "id": 2905,
  "curve_key": "4730429436771040185615233041:-325349375613823360305886530215745263066489",
  "ainvs": [
    "1",
    "1",
    "1",
    "-98550613266063337200317355",
    "376561777330773011672581883581427255577"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 191.1714404977108,
  "faltings_height": 13.517249902084579,
  "conductor": "23959330209511704615223770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "41",
    "43",
    "97",
    "193",
    "241",
    "2087",
    "2713"
  ],
  "discriminant": "246899560812734106019762632924125764840831090528827445414363867899337113600",
  "regulator": "14149092.41705754057574712136410584021807010042184555",
  "points": [
    [
      "12447532967411643/1849",
      "339313201431711916360322/79507"
    ],
    [
      "13780951070733988643/2380849",
      "-859850995256842220824791078/3673650007"
    ],
    [
      "209423712383438955/17161",
      "70780925375818346625725106/2248091"
    ],
    [
      "67282291476523/9",
      "204955008367285681202/27"
    ],
    [
      "719845077776728235/121801",
      "-31604987261507925908478258/42508549"
    ],
    [
      "54699710140459/9",
      "-39145560270981006542/27"
    ],
    [
      "408196342805737990635/77492809",
      "1294470641190950171649691248626/682169197627"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-054, rational kernel x=-45905215149213/4. Source: https://dujella.github.io/tors/z2z4old678.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 20:27:44",
  "updated_at": "2026-09-26 20:27:44"
}