{
  "id": 278,
  "curve_key": "1242091428912:-1534578842303594496",
  "ainvs": [
    "0",
    "0",
    "0",
    "-25876904769",
    "1776132919332864"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "naive_height": 83.7495752949018,
  "faltings_height": 4.950629962750487,
  "conductor": "2215450455430034397055968",
  "bad_primes": [
    "2",
    "3",
    "29",
    "1164682969",
    "7853546759"
  ],
  "discriminant": "-253845254197855645658231020687296",
  "regulator": "31350.737884554892910386288522170451896721726425949",
  "points": [
    [
      "0",
      "42144192"
    ],
    [
      "160863",
      "42144192"
    ],
    [
      "-121104",
      "55980324"
    ],
    [
      "75081",
      "-16016004"
    ],
    [
      "174087",
      "50470092"
    ],
    [
      "117852",
      "19061622"
    ]
  ],
  "submitter": "Daksh Shami",
  "commentary": "Rank >= 6. Found during a preliminary search among rational specializations of the classical one-parameter family y^2 = x^3 - u^2*x + 1, at u = 1849/1392. ",
  "created_at": "2026-08-21 20:23:25",
  "updated_at": "2026-08-21 20:23:25"
}