{
  "id": 3607,
  "curve_key": "340174836317063729172556201:-6393756260473378654624165118568382449301",
  "ainvs": [
    "1",
    "0",
    "1",
    "-7086975756605494357761588",
    "7400180857028782861538992503442851406"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 183.31228111328053,
  "faltings_height": 13.1688164774204,
  "conductor": "365003356408068742591136372104878505218862693766370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "37",
    "127",
    "104106275822577333713490695368930382973451"
  ],
  "discriminant": "-876999247192101508782630648574498083262013124456285007854728702009424487500",
  "regulator": "1178462672637185654537.67855178118693901583627609039728362243066022677236",
  "points": [
    [
      "1762190092190",
      "619463258219501547"
    ],
    [
      "-2018954010109598650/7612081",
      "63912943614770938412138314773/21001731479"
    ],
    [
      "-3101939222395897675/1008016",
      "264285443696287806257819643/1012048064"
    ],
    [
      "-261376175144903632/157609",
      "239018428640917345446280809/62570773"
    ],
    [
      "-220010246871592045/76729",
      "43277921786586608883051561/21253933"
    ],
    [
      "-16451602102426870/24649",
      "13312069757042350125489366/3869893"
    ],
    [
      "7009262823518780/4489",
      "113028324647704553022171/300763"
    ],
    [
      "527393293585440425/262144",
      "152162250385804505636840811/134217728"
    ],
    [
      "14114456354877330485/1281424",
      "51605913668621719243349211771/1450571968"
    ],
    [
      "7549225590518575850/4566769",
      "4388031331386599725724867886/9759185353"
    ],
    [
      "41049523397173768895/6466849",
      "242911863897926615109099406449/16445197007"
    ],
    [
      "322478938600488213500/196252081",
      "1203624253639314496925412245298/2749295402729"
    ],
    [
      "1679734830637804290020/772450849",
      "32359685977695611836070827903449/21468726446257"
    ],
    [
      "1940717828396173260500/451095121",
      "72041964312294245608236763111503/9580809274919"
    ],
    [
      "5415594328804961978402/3080361001",
      "104653267696638990196127823883014/170963115916501"
    ],
    [
      "10489102945600393147682/15210535561",
      "3161914144058694530910994841718693/1875930561273691"
    ],
    [
      "333770574810238191299861/213245386225",
      "37127429798052371354442968703332961/98473520677911625"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 5/18 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:18:15",
  "updated_at": "2026-09-29 19:18:15"
}