{
  "id": 686,
  "curve_key": "6108722256:-476369267037120",
  "ainvs": [
    "0",
    "0",
    "0",
    "-127265047",
    "551353318330"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "naive_height": 67.59895039456893,
  "faltings_height": 3.437325135267392,
  "conductor": "18597723997878981667496",
  "bad_primes": [
    "2",
    "431",
    "5393771461101792827"
  ],
  "discriminant": "595127167932127413359872",
  "regulator": "4550641.01475868708712299052195683486836946771091304033912667",
  "points": [
    [
      "6249",
      "9874"
    ],
    [
      "6765",
      "2650"
    ],
    [
      "6781",
      "13142"
    ],
    [
      "6201",
      "25022"
    ],
    [
      "6157",
      "34438"
    ],
    [
      "6121",
      "41198"
    ],
    [
      "6873",
      "36446"
    ],
    [
      "6901",
      "41822"
    ],
    [
      "6953",
      "51154"
    ],
    [
      "5949",
      "69226"
    ],
    [
      "6767",
      "5212"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "from the searches earlier this year that found Curves 157, 158, 244  of ranks 12, 13, 14; this rank-11 curve now appears also in M.Rubinstein's github tables.  It is not quite a record but has N very close to the curve (#50) from Elkies-Watkins 2004, and is one of several curves with N smaller than the second-smallest N from that paper (66484354768372183177742, for [1, -1, 0, -38099014, 115877816224]).",
  "created_at": "2026-09-09 03:46:11",
  "updated_at": "2026-09-09 03:46:11"
}