{
  "id": 6414,
  "curve_key": "72943674088662075973687609:-614953911865175048644455833868014907373",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1519659876847126582785159",
    "711752212806788927237642176798674046"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 178.65518936205552,
  "faltings_height": 12.764288563119068,
  "conductor": "414850321299557480517309911988570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "37",
    "101",
    "127",
    "139",
    "181",
    "307",
    "389",
    "457",
    "6607",
    "219217"
  ],
  "discriminant": "5757464444255877554859411996575730901726207849377939773138921716885326300",
  "regulator": "111929954.5766176467420428023844376990327264283089471711010",
  "points": [
    [
      "537979222703",
      "223404307043641158"
    ],
    [
      "-375367431673/4",
      "-7390949853275973651/8"
    ],
    [
      "631543126253",
      "-62533250986696692"
    ],
    [
      "1826733249965",
      "2007849798734572812"
    ],
    [
      "15796996413809/25",
      "7707281147894964138/125"
    ],
    [
      "397029522383",
      "-413506076024934822"
    ],
    [
      "3152443688459/4",
      "480143246322695523/8"
    ],
    [
      "-1402730294017",
      "288686864121826878"
    ],
    [
      "570535498838",
      "174492545916395253"
    ],
    [
      "105239076902453",
      "1079532842228677924158"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Specialization at t=466/77 of the Z/3 K3 family y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3, as posted in the Layr Labs Elliptic Rank Challenge repository (submission/board/3-r12-z3k3.ec, commit c8f82607a219df846ab80dd9e14ee09a2904d709). Sections from the same family, ellrank with 10 independent points, torsion Z/3Z (elltors), PARI/GP 2.19. Rank lower bound 10 is computed from these points; no upper bound claimed.",
  "created_at": "2026-11-02 13:32:39",
  "updated_at": "2026-11-02 13:32:39"
}