{
  "id": 2869,
  "curve_key": "3213456651758434081034881:-11406629292633382278796534611055350721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-66947013578300710021560",
    "13202117236838613534512612222145600"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 170.65451610213665,
  "faltings_height": 12.266144503904327,
  "conductor": "3673224997035980575470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "41",
    "43",
    "79",
    "109",
    "139",
    "1061",
    "2377729"
  ],
  "discriminant": "-56092628853366673399152173840721136214004124698027738359261204544000000",
  "regulator": "911949.95097188486849274806495046702179756793146659",
  "points": [
    [
      "12008964230250/121",
      "115539495422600008710/1331"
    ],
    [
      "191471517688320/1369",
      "4107159899026633817640/50653"
    ],
    [
      "174597191250",
      "82678862670862410"
    ],
    [
      "-880426296397440/4489",
      "41225323911384506238360/300763"
    ],
    [
      "-341738728226880/14641",
      "215170127300679481504440/1771561"
    ],
    [
      "-12774845320300800/63001",
      "-2147331886985192829797160/15813251"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-162, rational kernel x=163751652720. 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 20:26:07",
  "updated_at": "2026-09-26 20:26:07"
}