{
  "id": 4282,
  "curve_key": "1565495727262070581561:-49690798435969138501378659768941",
  "ainvs": [
    "1",
    "1",
    "0",
    "-32614494317959803782",
    "57512498176189722855223530564"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 146.4074684560307,
  "faltings_height": 10.20869490742335,
  "conductor": "246900641867205563351711407820506530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "67",
    "131",
    "149",
    "157",
    "163",
    "239",
    "311",
    "677",
    "821",
    "1051",
    "1489",
    "18199"
  ],
  "discriminant": "791380366031975076649049026230168075911784068575688756250000",
  "regulator": "126612352065026454.77418916507892316838525967692426429558041204",
  "points": [
    [
      "6824944803877/49",
      "-17815112297972151532/343"
    ],
    [
      "102680490950173/22801",
      "-152674329874979721799/3442951"
    ],
    [
      "9427998878913/256",
      "28615328558411259321/4096"
    ],
    [
      "3601919702213330893/4532641",
      "6835804068672501958497290964/9649992689"
    ],
    [
      "14199342146748030558147853/1485052660577161",
      "-45054995139190774860492362944073790309/57228555133065156194341"
    ],
    [
      "280150903961720392/277729",
      "-148279567376604672138795942/146363183"
    ],
    [
      "39890853157/9",
      "146617741568677/27"
    ],
    [
      "39202476797609431261/8844462025",
      "-4746598959134333858165055301/831777431141125"
    ],
    [
      "3341693078464345926913/639385747456",
      "-88284397931289521395517963234879/511263073837776896"
    ],
    [
      "119655895966589184913290472/10277292682182289",
      "1167646927897110363184898121837533548362/1041880925527618314854087"
    ],
    [
      "2347900497477270472197/132957224689",
      "108279873334224410741361639547212/48480591710024137"
    ],
    [
      "207444899079835308008356/46506739572225",
      "8873147077674243162779119781888366/317156663585652026625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from my curve#4259 by a rational 2-isogeny while searching for smaller heights and discriminants. The twelve rational points were transported through the isogeny to this minimal model. PARI/GP returned rank bounds [12,12].",
  "created_at": "2026-10-16 15:26:18",
  "updated_at": "2026-10-16 15:26:18"
}