{
  "id": 5057,
  "curve_key": "58371158941755580435399435774081200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1216065811286574592404154911960025",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 240.1563899487441,
  "faltings_height": 18.081272907370167,
  "conductor": "38914105961170386956932957182720800",
  "bad_primes": [
    "2",
    "5",
    "17",
    "19",
    "23",
    "97",
    "101",
    "5857",
    "16361"
  ],
  "discriminant": "115093609507936919409641053742415529011972910633773706133981948113516039062682310893225893115201000000",
  "regulator": "15918138125.45086627340207074840783990989792874748850",
  "points": [
    [
      "-4722990064421775862130820/343694521",
      "23939471560987507426068193596845052150/6371752724819"
    ],
    [
      "2467669623793536742981921/28601104",
      "3545680100603658249099354354497724081/152958704192"
    ],
    [
      "3671870380630485299038793787761/28433529936100",
      "6774694649450316290634485093304726949164662241/151616396013565391000"
    ],
    [
      "-6420836488965006020/20331081",
      "1796531412254699582287070437921850/91672844229"
    ],
    [
      "-1000948660184917398285646663680/737889578359129",
      "25724502872104818407018516038834945456953076800/20044123266965518328867"
    ],
    [
      "24856833666144819741201/712336",
      "141274038084225440328532814139399/601211584"
    ],
    [
      "427892760906119427997965080177854973820/8344855487796500830249",
      "6489122984768962278367243549095461743978310452263572831850/762304055532282660916046557268693"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 34872135169596005, 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 01:50:34",
  "updated_at": "2026-10-21 01:50:34"
}