{
  "id": 102,
  "curve_key": "17012350498427222055155079825:-2213556462276218875887383925532094329805625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-354423968717233792815730830",
    "2561986646153119712343318111147387184797"
  ],
  "rank_lower_bound": 18,
  "naive_height": 195.01121127308886,
  "faltings_height": 14.057836969831294,
  "conductor": "2300421877446970281453428041661531850670855338680544890937950",
  "bad_primes": [
    "2",
    "5",
    "11",
    "19",
    "29",
    "31",
    "67",
    "97",
    "1194256489",
    "31549128016279775676380684297728489659559"
  ],
  "discriminant": "13821441904429578871006127124264988888315125425652332382713954798587645696000000",
  "regulator": "28029078662856042.835630945014296244921316895372976514932855516252265257542",
  "points": [
    [
      "18767601803769",
      "-50206358006201696685"
    ],
    [
      "10063361108249",
      "3797268895762353875"
    ],
    [
      "14463240795049",
      "-21479423046961879325"
    ],
    [
      "11845650903449",
      "5077316719636289875"
    ],
    [
      "10180034695969",
      "-2987808036154910885"
    ],
    [
      "27862066360089",
      "119650218507818587155"
    ],
    [
      "11579125906089",
      "-3248326623828937245"
    ],
    [
      "101778703261921/9",
      "-10313188444042479295/27"
    ],
    [
      "11565547025193",
      "3147828265004909171"
    ],
    [
      "11951310161719",
      "5762553083670604165"
    ],
    [
      "12606449162989",
      "9869546987446928155"
    ],
    [
      "2192939908113",
      "-42371005295704069429"
    ],
    [
      "5454584277089",
      "-28125412966729382245"
    ],
    [
      "29333052772769",
      "131926590527912797315"
    ],
    [
      "471775179472089",
      "-10239102436034213707245"
    ],
    [
      "75605547614289",
      "638703266730899417355"
    ],
    [
      "-192585037525199/9",
      "503686169623613931185/27"
    ],
    [
      "562483151941701/49",
      "848706767424556824125/343"
    ]
  ],
  "submitter": "Alexey Pozdnyakov",
  "commentary": "Generated with assistance from OpenAI Codex, based on GPT-5, during a local generalized Mestre/Fermigier quartic-family search. I searched nondegenerate Mestre (u,v) families in the box [-3,3]^2, focusing here on denominator bands 41<=n<=60 and 61<=n<=80 for specializations T=m/n. For each family I used a Mestre-Nagao sieve at prime bound M=200, rescored per-family survivors at M=1000, computed exact minimal-model heights for the global top rows, and certified the top unique models by height and score using GP famcert. This rank >= 18 conductor candidate came from family mestre_u3_vm1 at T=101/62 in the n=61..80 band; famcert certified 18 independent points, and Sage computed log conductor 138.988198, below the current ICARM rank >= 18 conductor frontier if accepted.",
  "created_at": "2026-06-23 23:58:09",
  "updated_at": "2026-07-01 22:32:42"
}