{
  "id": 4817,
  "curve_key": "0:827464872201878656800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-957713972455878075"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 96.32979665946334,
  "faltings_height": 6.08513896408024,
  "conductor": "1811784796122900519742721223240900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "383",
    "5147",
    "719745749"
  ],
  "discriminant": "-396237334912078343667733131522784830000",
  "regulator": "325000571244403.679120213292647764596854595231775236636623743",
  "points": [
    [
      "26958065363891569/26264091844",
      "1496827338729706559743703/4256411252422328"
    ],
    [
      "110547533499334791/99394542361",
      "20262061490128858075431186/31336017975610109"
    ],
    [
      "1127535742283359/946731361",
      "24915942868028967021698/29129977246609"
    ],
    [
      "1160358586476819/874207489",
      "30372556630445621001828/25847692827263"
    ],
    [
      "31501677604580961/15792446224",
      "5242972603966263674958609/1984605132077632"
    ],
    [
      "1264378611596809/620209216",
      "42341726548261119276827/15445690315264"
    ],
    [
      "32614718148726369/12681462544",
      "5721864699588497338606353/1428084860004928"
    ],
    [
      "1336924496906329/406344964",
      "48221549865845866775683/8191101784312"
    ],
    [
      "1388531816658339/209409841",
      "51655814114267622975012/3030369809111"
    ],
    [
      "35177277436012671/2782879009",
      "6596147328655475029091994/146805216361777"
    ],
    [
      "5631601144272171/424566025",
      "422531122769276938080156/8748182945125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of y^2=x^3+35470887868736225, attributed to Noam Elkies (1999) in source curve #4699, submitted by jesper-petersen: https://elliptic-rank.icarm.cloud/curve/4699. I transported its eleven supplied rational points through the degree-3 isogeny and checked them exactly on this minimal model. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:52:54",
  "updated_at": "2026-10-20 21:52:54"
}