{
  "id": 743,
  "curve_key": "647198595038671238745079713221762161:-517778147741239284877548251286919497966343455541734409",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13483304063305650807189160692120045",
    "599280263589397319336516618899204444269356349200337"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 247.3738837911456,
  "faltings_height": 18.454577087433137,
  "conductor": "45338571294080722176878229370326088934964788929204379574261910884085409670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "43",
    "79",
    "1417216780984163857",
    "8269459002193140764341761594260750978809385681"
  ],
  "discriminant": "1733385586882379368494476030773071654575790685170142154042556620709636153875714478480507056455680000000",
  "regulator": "95359065071160900193.694518373815593526344579247838909774233441621416310292714223",
  "points": [
    [
      "-533719755788960769/4",
      "-38224848201243041884427931/8"
    ],
    [
      "-38439035239881261204/289",
      "-30933927645462784115782637691/4913"
    ],
    [
      "-120920185710088926",
      "-21485489602278401653400097"
    ],
    [
      "-111413144306344986",
      "-26805570302522205506907357"
    ],
    [
      "-65401811258844606",
      "-34660687573115795950916577"
    ],
    [
      "-6624992471499486",
      "-26235782376872039382925857"
    ],
    [
      "7369784481944514",
      "-22367644022971252363333857"
    ],
    [
      "33967338182387514",
      "-13434252964201562832852657"
    ],
    [
      "471830284751756626/9",
      "-163118499258052265590990139/27"
    ],
    [
      "1367599802403035921181/21904",
      "-2949760808712816650870433307269/3241792"
    ],
    [
      "71504436466585794",
      "-870703794752315588766177"
    ],
    [
      "81554049290029602",
      "-6487167028781214493385217"
    ],
    [
      "85711538805090114",
      "-8560525219221954681417057"
    ],
    [
      "139305361788954354",
      "-37740446679289345255319937"
    ],
    [
      "265234181194617474",
      "-125227999737500033851985697"
    ],
    [
      "487601640204954114",
      "-331594183488259751005353057"
    ],
    [
      "1734542422054581594",
      "-2279434392197401309764235377"
    ],
    [
      "89830776010866114",
      "-10628272742536628964345057"
    ],
    [
      "62629929195306114",
      "-698773983246511953825057"
    ],
    [
      "130165708221295014",
      "-32397971629514525792907657"
    ],
    [
      "1454763576490114554",
      "-1749215349434241888157403337"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-19/74 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 21 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 18:15:55",
  "updated_at": "2026-09-16 18:15:55"
}