{
  "id": 4178,
  "curve_key": "5030532836378231803969:-330538671571802481916891279597153",
  "ainvs": [
    "1",
    "0",
    "0",
    "-104802767424546495916",
    "382567906903074864192504550800"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 149.90943858918533,
  "faltings_height": 10.450960557078147,
  "conductor": "2451861563535401352551788293184551769586091703999331590",
  "bad_primes": [
    "2",
    "5",
    "13",
    "359",
    "6991",
    "7514824498054176890848361843367171577531611947"
  ],
  "discriminant": "10444537962810644097654209842839281010153616884364512680345600",
  "regulator": "48204073880141782.4472260602068196246649156400378942673354952246298112431",
  "points": [
    [
      "18752694488",
      "2238711855562516"
    ],
    [
      "21187973464",
      "2770175542369556"
    ],
    [
      "5913133578564062/38809",
      "453698198113930383252048/7645373"
    ],
    [
      "-6383223220004312/654481",
      "-365670735423731646107996/529475129"
    ],
    [
      "-1530870946186274/229441",
      "97361525705588433655470/109902239"
    ],
    [
      "-173594593045048/16129",
      "1052047502980306959468/2048383"
    ],
    [
      "3246408396450/29929",
      "3154590217705496061600/5177717"
    ],
    [
      "2437526089519/324",
      "-823134173747791807/5832"
    ],
    [
      "12988664678197784/1692601",
      "382800160087082217502340/2202073901"
    ],
    [
      "18305267322239704/2181529",
      "987720064982452149022212/3222118333"
    ],
    [
      "-870988385819054/450241",
      "-229697769260175201998030/302111711"
    ],
    [
      "3640110638",
      "-222054021516734"
    ],
    [
      "-11949973886600/6561",
      "-400316009841752415020/531441"
    ],
    [
      "-136169728052/121",
      "-940296378034769204/1331"
    ],
    [
      "-152733408719/64",
      "-402850714239995925/512"
    ],
    [
      "4707618479604/5041",
      "-191243437389252965604/357911"
    ],
    [
      "2623987560800350084/45954841",
      "-4186097433772416582558366260/311527867139"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-1524, -1034, 94, 254, 780, 1430], T = 149; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x) = prod(x - a_i), on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by a discriminant-first sweep + Nagao-sum rescoring + ratpoints search on the quartic.",
  "created_at": "2026-10-11 22:59:01",
  "updated_at": "2026-10-11 22:59:01"
}