{
  "id": 747,
  "curve_key": "432424935378114413288366018077268800:-307551857854869544540540187743739922708659683757974400",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-9008852820377383610174292043276433",
    "355962798443136049924872453718086113933860870626837"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 246.32096691830932,
  "faltings_height": 18.485460643914713,
  "conductor": "7984751558079104972746782605220711236089923859646184489024403069751133842847257245758600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "31",
    "37",
    "179",
    "319299082519787340784137635167614330086839330734305269554690287558269650592729"
  ],
  "discriminant": "-7944695459732437794258110307402026108921956919186644034086453498110776104724727287158376831845617120000",
  "regulator": "1286297487816386348465066.97909869307465905933163265860626281918944099574451945938596",
  "points": [
    [
      "-105652498745225204",
      "-11332688261765523757302667"
    ],
    [
      "-112594212876235333059/1156",
      "-691368183348862264732081445913/39304"
    ],
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      "-89379357041858719",
      "-21145830104118905588197662"
    ],
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      "-88832627114312483",
      "-21336439925194675774211110"
    ],
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      "-18099196062247541387/5476",
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    ],
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    ],
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      "43944912659539441",
      "-6703282868687028253698782"
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      "51732721016935567",
      "-5325531610642952586102890"
    ],
    [
      "54385118623382981",
      "-5183856791272161513065562"
    ],
    [
      "59230032692925753",
      "-5491699273711842605114334"
    ],
    [
      "4862091075633258457/81",
      "-4090072609930847120451493010/729"
    ],
    [
      "64598371354223487",
      "-6600857913383360634079590"
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    [
      "69327461585073717",
      "-8038051155726627072252390"
    ],
    [
      "74816558509246457",
      "-10036853311789776331911390"
    ],
    [
      "19236333393702502457841113/191462569",
      "-57129637060086314248905021399682128330/2649267567253"
    ],
    [
      "195795355353649690035833/923521",
      "-79258735128673286134461149166123426/887503681"
    ],
    [
      "449372309716068757",
      "-295045494114446425533331610"
    ],
    [
      "1429164186649133045620993/1108809",
      "-1704035906006108572907176519764547030/1167575877"
    ],
    [
      "1368884612047286177",
      "-1597842789412810878908367390"
    ],
    [
      "1659703404809362511",
      "-2134771295486976674218360278"
    ],
    [
      "28627737110604222417/16",
      "-152961499763686917114117614385/64"
    ],
    [
      "3821931069398266388",
      "-7469502814875966528861791769"
    ],
    [
      "7724069905544843652",
      "-21465285514579307736337043265"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-43/75 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 18:18:25",
  "updated_at": "2026-09-16 18:18:25"
}