{
  "id": 5553,
  "curve_key": "2748981978330243074723728:-4505921838239924558676079368708264640",
  "ainvs": [
    "0",
    "1",
    "0",
    "-57270457881880064056744",
    "5215187312758600308803354062800836"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 168.8198186559011,
  "faltings_height": 11.939175155801014,
  "conductor": "81436544373824749184208",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "71",
    "277",
    "317",
    "389",
    "449",
    "403957"
  ],
  "discriminant": "272254380799695876104541011098568688781908365670570076769588394230784",
  "regulator": "115034071.6193711234838073841728798398542450870025077",
  "points": [
    [
      "88100139422",
      "29213919217278180"
    ],
    [
      "-7347612617538150977/43811161",
      "29147379936696185358867290310/289986074659"
    ],
    [
      "3217669312462/9",
      "4710542063154107660/27"
    ],
    [
      "21698590104392/961",
      "1868439353592953632590/29791"
    ],
    [
      "146696106774420611/954529",
      "6148311630908012902490700/932574833"
    ],
    [
      "75753174210839686304/1309933249",
      "2170883305584335368997209442994/47410414081057"
    ],
    [
      "181846221953439475994/518700625",
      "1984719405689773077657962255472/11813406734375"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (155211,652703) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.",
  "created_at": "2026-10-23 02:09:24",
  "updated_at": "2026-10-23 02:09:24"
}