{
  "id": 757,
  "curve_key": "785927250452545532702721:-674607502534167435095124346295060481",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-16373484384428031931307",
    "780795720529750124678426853231739"
  ],
  "rank_lower_bound": 15,
  "torsion": [],
  "naive_height": 165.06345355303316,
  "faltings_height": 11.672972270473299,
  "conductor": "3054168934820674430483080510377005677651470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "73",
    "220373",
    "2391691",
    "5218639",
    "142342930229587"
  ],
  "discriminant": "17568028278748740019130613693715009952376436328232487394688000000000",
  "regulator": "192195642747.09885966199645188977448434695495390906019581825202936000",
  "points": [
    [
      "-94254393293",
      "-38557997863419934"
    ],
    [
      "-78384948053",
      "-39782087940793174"
    ],
    [
      "-65031102053",
      "-39630284759368774"
    ],
    [
      "-54552803453",
      "-38880116712586774"
    ],
    [
      "-37480069973",
      "-36630907006969174"
    ],
    [
      "-22646416853",
      "-33763608557410774"
    ],
    [
      "-21100121333",
      "-33419805945963094"
    ],
    [
      "3196379467",
      "-26990601964671574"
    ],
    [
      "12519267547",
      "-24036933256144774"
    ],
    [
      "23576174287",
      "-20195954085152074"
    ],
    [
      "24043496197",
      "-20025476029594924"
    ],
    [
      "605177449681141/16129",
      "-30331901332259444934244/2048383"
    ],
    [
      "196136852848507/1681",
      "-1476285749311221318854/68921"
    ],
    [
      "246903079183/4",
      "-18433845672924017/8"
    ],
    [
      "38361931847",
      "-14461419460299074"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = -19/165 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 15 points with an exact independence certificate, proving rank >= 15.",
  "created_at": "2026-09-18 01:25:10",
  "updated_at": "2026-09-18 01:25:10"
}