{
  "id": 1379,
  "curve_key": "4684873187531432744073185346599583374650580339874117184:3039800110631020823813049639863180278853726858708529434845856832163962336640010752",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-97601524740238182168191361387491320305220423747377441",
    "-3518287165082200027561400013604098557482789808182196013018931231782963307170495"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "naive_height": 377.6518016077192,
  "faltings_height": 29.533524622754758,
  "conductor": "14545260576720879419495082714314736176851942086001467334920374959680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "37",
    "43",
    "47",
    "53",
    "59",
    "61",
    "617",
    "1117",
    "1277",
    "2309",
    "6173",
    "8521",
    "9811",
    "29753",
    "123953",
    "138433",
    "94669559"
  ],
  "discriminant": "54157051118179130527736222739761783293061542708942220779193282013833702442568863224692098719145235621645054138628319435028226712175831278442044594117961359360000",
  "regulator": "24244457340333466466809.30021283425902878900891007528826689311457",
  "points": [
    [
      "63996513289110046994410704592435663881/22755119104",
      "-508748927894805897539914008878884820541747394626725223909/3432564206600192"
    ],
    [
      "23383414360373338107390906074184698461/48778256164",
      "-83349469063302852829462519210596263228410674672436589319/10773068099868712"
    ],
    [
      "-45540455300446384515602760687/256",
      "11739704608435474787688287455022316121484025/4096"
    ],
    [
      "-118398332881652495834200290367110029554523/463541675080324",
      "21745411748547054554406051071469858855169213980146671812889875/9980060608229527165832"
    ],
    [
      "65827299195320580571642185155641757657407514264507546716369/178094078605383224838048669552400",
      "-7848011296843765164932590672673357240830384119925263156372494402803989336231874870792497/2376699199888409693780028721727012766692256232000"
    ],
    [
      "9263201683455194850504487899541363779597060961489/1746017985421513441936",
      "-28143768677441788894771152083878090828966829270753229081781891262465086833/72958025084497190704950287125184"
    ],
    [
      "3786492031119961168925327368332680335265215664497016929/3765048822777954990638223616",
      "6990157241485356566286331758540068665536587331324517181378813724839337040417641873/231023371920486669121230170688660925681664"
    ],
    [
      "9983610142661677060700635773690280920990956272490784973789/10970873006342981084351318628100",
      "-934432793930775596327101108554468424965837788876394363440002165841977190661243723140937/36338063696209177275161711182559955253949429000"
    ],
    [
      "28344176867652682821089242581843974060085233679500547229921/48782451571798052919039740928400",
      "-3972366999522977420182927076206783231552964406671689253799501285480179380808108608496919/340718278775168930795554701604580558868178952000"
    ],
    [
      "10788559734768684928380892815764494907056441/7651172342160400",
      "-34532525341906542174883784825894974739060058283293458704241217189/669255542917665505192000"
    ],
    [
      "-19207326906323176003206145888162255674811881691023/492354474131017107356224",
      "165645545492761958324987655593965649647937666962226033155629696496092904425/345475165221626947743461757940602368"
    ],
    [
      "-108222337138751910390962655195477995060020572416305523/373342748396538473984373849",
      "4656317182751804040449631605325950759188357083400803172007407117425719817516800/7213758189835125004852930368874149926493"
    ],
    [
      "64887350462370885994670274771783841568752810245887199280912408441631536556701/2408665923357544321728690772935893009619320508900",
      "-16527638925702452814162935415120510325725029320088315616682497469841450000526721164355727726185973978177513968699399/3738219965926677578662969463476632515057170966612179787776351054366063000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Obtained from ICARM curve #803, a rank-at-least-13 curve with torsion \\(\\mathbf Z/4\\mathbf Z\\), by quotienting by its unique rational point of order 2. The resulting 2-isogenous curve has global minimal model with ainvs \\([0,-1,0,-97601524740238182168191361387491320305220423747377441,-3518287165082200027561400013604098557482789808182196013018931231782963307170495]\\), torsion \\(\\mathbf Z/2\\mathbf Z\\times\\mathbf Z/2\\mathbf Z\\), and the same conductor \\(14545260576720879419495082714314736176851942086001467334920374959680\\). The thirteen independent source points were mapped through the isogeny to thirteen independent points on the quotient. The isogeny, minimal model, conductor, torsion and mapped points were verified in Magma.",
  "created_at": "2026-09-24 19:11:33",
  "updated_at": "2026-09-24 19:11:33"
}