{
  "id": 5058,
  "curve_key": "103884493350399488746632250213856448:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2164260278133322682221505212788676",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 241.88576312959418,
  "faltings_height": 18.225387339107673,
  "conductor": "34628164450133162915544083404618816",
  "bad_primes": [
    "2",
    "7",
    "23",
    "41",
    "73",
    "79",
    "193",
    "1297",
    "2441"
  ],
  "discriminant": "648796412806690626353528480103581576354921370438993521336666615049859843606598600913106984945163505664",
  "regulator": "1930965131.396565564876709092621728318000168197247271",
  "points": [
    [
      "467885694620490752",
      "318458030287945869750849216"
    ],
    [
      "-115013181850350992/9",
      "136532037582074453462746408/27"
    ],
    [
      "-10779212024424390123809118/283686649",
      "25000474387539043229812326098929573344/4778134229107"
    ],
    [
      "-26096018576302086561170192/2634460929",
      "611728358246959024244811382942260631672/135218976102783"
    ],
    [
      "-1024153500246870387796185512862/67312359856921",
      "2994794101465844979067527390125953030127995392/552258265646081078531"
    ],
    [
      "-9466623698437582",
      "4431689018989664882695008"
    ],
    [
      "-1148973251350491248192/29929",
      "26657526734467803627821948369328/5177717"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 46521610872080974, rank 7 example from Watkins, Donnelly, Elkies, Fisher, Granville, Rogers, 'Ranks of quadratic twists of elliptic curves', Publ. Math. Besancon 2014, doi:10.5802/pmb.9; points from https://magma.maths.usyd.edu.au/~watkins/PTS.r6r7.",
  "created_at": "2026-10-21 01:50:38",
  "updated_at": "2026-10-21 01:50:38"
}