{
  "id": 4079,
  "curve_key": "11416492325208472404740587194261793719939030406382001:-1025662925164745011661103149125787986455583329798184758278616530783398831073001",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-237843590108509841765428899880454035832063133466292",
    "1187109867088825244978128704282411400339941147142161032935981794570643124759"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
  ],
  "naive_height": 359.6006962435056,
  "faltings_height": 27.96393563962565,
  "conductor": "59922190121336398795572364641929095928611712492963586620439649207478009865597394590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "31",
    "79",
    "89",
    "103",
    "151",
    "167",
    "229",
    "263",
    "283",
    "307",
    "313",
    "479",
    "2381",
    "2621",
    "3919",
    "5431",
    "10459",
    "12101",
    "13441",
    "14851",
    "16481",
    "35509",
    "260111"
  ],
  "discriminant": "252314177355834588647381366058696061681393231871640909455867016287591582767500657939435797429942358280353320453798376954890322537767229523376640000000000",
  "regulator": "691585808662145698497.025991104914093588882682474311012986273756590247057429169",
  "points": [
    [
      "47067844897071791209417",
      "34291619765667107220961491959410673541"
    ],
    [
      "5814412815903811632520917",
      "871325108938918635965997094824804541"
    ],
    [
      "5816962178859076360268517",
      "641508506725873816768148739320214541"
    ],
    [
      "5681684708223842824309167",
      "4378483388165924164886086401654804541"
    ],
    [
      "5781908735448751194342417",
      "2282948607239853703861815471121478041"
    ],
    [
      "5805311356758763706695917",
      "1415021355465625977424510976276679541"
    ],
    [
      "671077204855498227518997",
      "32059330489755416601952661436907512061"
    ],
    [
      "11989358974451671095290917",
      "7676251532810749960821688176141854541"
    ],
    [
      "1562293871267413317586917",
      "28624141413758987900969794922124054541"
    ],
    [
      "1576322062238846728594867",
      "28567614529331320357493343879981604341"
    ],
    [
      "2645057615249834709978417",
      "24010530256918791161702085809168042041"
    ],
    [
      "3720489485435437102441417",
      "18807298122579603431575117122003441541"
    ],
    [
      "3816536637918617509199667",
      "18301982965535924241809674496531960791"
    ],
    [
      "4512681870129300042673917",
      "14342071221839135668437887977558521541"
    ],
    [
      "4578423758711455665926277",
      "13933193381599661569174839553353688141"
    ],
    [
      "-4756917288381900348953883",
      "47019904101052608363476683373565059341"
    ],
    [
      "-7423289545094572164623783",
      "50434409310156378282912115980862469541"
    ],
    [
      "13282176913295608720023909",
      "19267088965938182571829569054014801293"
    ],
    [
      "15542115915720838350209667",
      "35282145912077658427145516554287410791"
    ],
    [
      "-17329093872184303283521083",
      "10239155062825108632969670098428466541"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -12396/65165 of the rank-9 fibration of X720 given by:\ny^2 + (504T^2 - 8334T - 1499)xy = x(x + (445T - 87)(127T - 4)(25T + 3)(89T + 168))(x + (583T - 196)(T - 13)(5T + 22)(253T + 29)).",
  "created_at": "2026-10-09 05:31:20",
  "updated_at": "2026-10-09 05:31:20"
}