{
  "id": 746,
  "curve_key": "63494009464160574372331099509911977825:-559932048929540671579872159075041465316121443725388180625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1322791863836678632756897906456499538",
    "648069501075857258662767528794908106200954623218194692"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 261.3348209136959,
  "faltings_height": 19.74864277212767,
  "conductor": "156889111317058904627359095900392258545849757386739107494369298910894227152978519034867350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "37",
    "43",
    "61",
    "167",
    "687437",
    "567870619",
    "15899278987",
    "5211124590731",
    "5947074660082643",
    "1051719181626496323255151"
  ],
  "discriminant": "-33303520599931763950103061542094412347814978171853250595158989021069462122510537288328566558809969494784000000",
  "regulator": "1092579385675086141050592.58990996787279366142638341295644428862945670587312542153993",
  "points": [
    [
      "-5101196395664243133/4",
      "-4086221822197997251602095169/8"
    ],
    [
      "-338762010068116138668/289",
      "-3767403259393871212660075448514/4913"
    ],
    [
      "-1077079444779710148",
      "-907359588065482822411666626"
    ],
    [
      "-1076035859747408082",
      "-908597516919788045795504448"
    ],
    [
      "-1007856131996937352371/21904",
      "-2729344267250968542465334696941927/3241792"
    ],
    [
      "241620708906401796",
      "-585287576597754868962497826"
    ],
    [
      "451874339617101732",
      "-377627080567319627565909666"
    ],
    [
      "525828187343488308",
      "-312885388772960289278028258"
    ],
    [
      "611580663717714948",
      "-260433573676335394503267618"
    ],
    [
      "667656413423496468",
      "-250033894769071173732350898"
    ],
    [
      "710734819374025428",
      "-258725110293189064669757538"
    ],
    [
      "329856858657298250212/441",
      "-2571844791601072222814894501626/9261"
    ],
    [
      "866040525691648982",
      "-389911807976427593793449416"
    ],
    [
      "898323614285423802",
      "-429777034195379732476805676"
    ],
    [
      "2110078476439023072",
      "-2692926671841316104484851486"
    ],
    [
      "5825073519692283132",
      "-13805654064555492917727665466"
    ],
    [
      "17156981670173602932",
      "-70910624993846436810357194466"
    ],
    [
      "23038188017256988668",
      "-110444005757930503358044070970"
    ],
    [
      "95032458423261948803/4",
      "-925356287126559163321447127153/8"
    ],
    [
      "26714057554857724302",
      "-137947650352506942121442146926"
    ],
    [
      "496511762101644132484/9",
      "-11061161963255899007185913021462/27"
    ],
    [
      "103979339573820672932",
      "-1060215472824303737906197026466"
    ],
    [
      "525581240898183779472",
      "-12049214757958794746582280691086"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-47/80 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 23 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 18:17:57",
  "updated_at": "2026-09-16 18:17:57"
}