{
  "id": 739,
  "curve_key": "838508179420176853347261250228357696:-831886882124127516325822096666403930340634105546447744",
  "ainvs": [
    "0",
    "1",
    "0",
    "-17468920404587017778067942713090785",
    "962832039495517952887468773316368993353086347426275"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "naive_height": 248.3110724305777,
  "faltings_height": 18.65232649218201,
  "conductor": "983631275147347131453459375659466622093811631944182198659688972050478637343069240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "37",
    "53",
    "89",
    "157",
    "211",
    "20327",
    "114407",
    "49217265343",
    "852073668103103",
    "77739055503716341272673923084877"
  ],
  "discriminant": "-59307908241598546438865701982056710913996630831929085812610204578814452759852694747757025704437740000000",
  "regulator": "10702107244251528767200.97852301754228020298401664062209722482669133270779476688721",
  "points": [
    [
      "-147078316185017770",
      "-18722412492129051263827875"
    ],
    [
      "-156704864824627310155/1156",
      "-1139056768486310154472297960335/39304"
    ],
    [
      "-124399349263052905",
      "-34797267093289670832579090"
    ],
    [
      "-123708859458443245",
      "-35080856353985570556827850"
    ],
    [
      "-25535954732985941395/5476",
      "-13094395625225531805953617450125/405224"
    ],
    [
      "27011635681505975",
      "-22598150012360131146882030"
    ],
    [
      "61119219521704655",
      "-11111242447563485342968050"
    ],
    [
      "711360060829812075509105/10699441",
      "-341634616478075969027554341320116050/34997871511"
    ],
    [
      "682238096699718355/9",
      "-232586479820857835681278930/27"
    ],
    [
      "4104520999781999287/49",
      "-3204691722228926977751820642/343"
    ],
    [
      "96769367784292355",
      "-13362412465338196771730250"
    ],
    [
      "104115882234869855",
      "-16512671435792596407947250"
    ],
    [
      "154623454275178223",
      "-44255265996059389191349746"
    ],
    [
      "205672371786027215",
      "-77911041295717724245178610"
    ],
    [
      "445644380301676055",
      "-285801321993460832995757550"
    ],
    [
      "629153264306216795",
      "-488888893310436223238626710"
    ],
    [
      "1911520121723369855",
      "-2636681920820841174723947250"
    ],
    [
      "2337185248428664505",
      "-3567472069097739239151628650"
    ],
    [
      "40160990927514442385/16",
      "-254165719267437506048507684895/64"
    ],
    [
      "48594219428965341070/9",
      "-338647667009430679255613009125/27"
    ],
    [
      "10848171928786689230",
      "-35727511464007371210995760375"
    ],
    [
      "21522522899528216255",
      "-99846213496374004425756740850"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-27/47 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 22 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:42:40",
  "updated_at": "2026-09-16 17:42:40"
}