{
  "id": 6437,
  "curve_key": "2030777491524104750255444206297:-2894045018484122827394687395257804029231678749",
  "ainvs": [
    "1",
    "0",
    "1",
    "-42307864406752182296988420965",
    "3349589141764027524569965404051711395908992"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 209.35796873723996,
  "faltings_height": 15.102855746916111,
  "conductor": "143404793018081973616765790502250200794",
  "bad_primes": [
    "2",
    "11",
    "31",
    "67",
    "103",
    "131",
    "271",
    "349",
    "601",
    "3163",
    "6679",
    "10069",
    "6024637"
  ],
  "discriminant": "-262727265585746560745305119108160496400999117811645133581949225065318043073250193776",
  "regulator": "19349747903205.5663621036045540308400783302687108669958890816",
  "points": [
    [
      "4537772888289827675315456265/38030704945216",
      "3352814559131065464712126009534372610487/234531706449472331264"
    ],
    [
      "3945224115069458560/33489",
      "124097174918179272953834521/6128487"
    ],
    [
      "-24959491794559668832/113569",
      "-54564631148807883826854753440/38272753"
    ],
    [
      "51552167053679035096/289",
      "-370143477645643500111454952273/4913"
    ],
    [
      "225834499799283868035/1570009",
      "963984760734464930077557721866/1967221277"
    ],
    [
      "119574724983962113039/881721",
      "-269764390976755297801898929534/827936019"
    ],
    [
      "426135384159409199388256111/3585641429241",
      "65723517043249284044332409034126193154/6789695311940743539"
    ],
    [
      "346157091803402994174384/3062404921",
      "-18221232676133545915622609858059344/169470425923219"
    ],
    [
      "35104759486535938363223/301265449",
      "-225004030163890186035452036009074/5229064398293"
    ],
    [
      "24971818700143105255/210681",
      "1009011820797620222674849534/96702579"
    ],
    [
      "43809960792356754343951/256736529",
      "4312412702949836209957107970775962/4113689404167"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -1094/737 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-11-03 04:34:54",
  "updated_at": "2026-11-03 04:34:54"
}