{
  "id": 1925,
  "curve_key": "-12505264530052061745631349999:-1276749889282412605271460896389006178601195001",
  "ainvs": [
    "1",
    "0",
    "0",
    "260526344376084619700653125",
    "1477719779262051648182126957716549533620625"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 207.72129376911874,
  "faltings_height": 15.36776592918797,
  "conductor": "171427577232061947088270456975440421292364577170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "41",
    "43",
    "269",
    "283",
    "349",
    "463",
    "12791",
    "29101",
    "179743",
    "244303",
    "113982049"
  ],
  "discriminant": "-943340413990995819810054337492191784520981404953867345098072182279654926340346964480000",
  "regulator": "15371003679745.84402822975186774131934082571792689360933507399765",
  "points": [
    [
      "5584476019667550",
      "-417327789442800665326575"
    ],
    [
      "-58305292862941665453958427701619948775586/541787672309704677001559569",
      "5686669873354107031033738466589421761657244310837052363741961/12610830210601839289639846606341294725753"
    ],
    [
      "11268052774694070",
      "-1196117874547760114368095"
    ],
    [
      "-12202233466291066852570312001720345077657478423186476240073118450/588117879598703661563577583019799401036271570998521",
      "17253434667612393343378490631633158970948211102010895853925679821119333425265264767913055385370275/14262530105328389262981812536733882634539980635096142043648687700385224834931"
    ],
    [
      "20605208403792864557206158/63057738769",
      "-95604971612599259978641677537138606423/15834617955499897"
    ],
    [
      "222221773767824220905386940550/567353859894481",
      "-106124344283771835014689129625886171838884825/13513909953413882784871"
    ],
    [
      "20451123681450",
      "1221311369699641134825"
    ],
    [
      "-40320279417417401697615281898/404666370575041",
      "-5536502588110723937714103952480601006255703/8140398608392479344161"
    ],
    [
      "40060086633999151723025146050/31678312465801",
      "-8021614597424081654005019802520033896098775/178296598288578592549"
    ],
    [
      "-26598357756817677261954/502432225",
      "-12917306612126619735567406461586401/11262018323375"
    ],
    [
      "247166244173218070/3481",
      "-279662226044493375306590525/205379"
    ],
    [
      "261049607048584072636366/1113490161",
      "-141117483862575071404634794353617927/37156053182409"
    ],
    [
      "-19595959995726677284402131257804825765154090550678461173736884130/189727779432349943783927274081075592660363486848409",
      "1543866627561163608098910444217112922700408749731305888937524200063252911013480498701948526425325/2613342827042063237932839628896869050153228953538372134994308656306508362173"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-8 family (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12) with u = (s^2 - l)/(2s), (p,q,s) = (2,3,115/9).",
  "created_at": "2026-09-25 19:16:11",
  "updated_at": "2026-09-25 19:16:11"
}