{
  "id": 4951,
  "curve_key": "-47735316211584:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "994485754408",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 94.490077865009,
  "faltings_height": 5.942413567058907,
  "conductor": "3956007662881795565721856",
  "bad_primes": [
    "2",
    "17",
    "101",
    "229",
    "409",
    "773"
  ],
  "discriminant": "-62947092241037302440104465748063059968",
  "regulator": "282749165670.81583441832620789200777929161702412186176046",
  "points": [
    [
      "116409933721/363609",
      "129936011154021287/219256227"
    ],
    [
      "248620907161/729",
      "123967638080870617/19683"
    ],
    [
      "14624790489",
      "1768619792317959"
    ],
    [
      "841374199615401/337126321",
      "26281477099171695321873/6189976379881"
    ],
    [
      "73209748329/6889",
      "19895606135666319/571787"
    ],
    [
      "1020538387089/1605289",
      "1917880790891344539/2033901163"
    ],
    [
      "1275418369/10404",
      "373321346269121/1061208"
    ],
    [
      "261666010089/99856",
      "143215846171853301/31554496"
    ],
    [
      "658589569/576",
      "22426683030719/13824"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4690, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4690.\r\n\r\nThe source model is y^2 = x^3 - 248621438602*x. Renshaw's commentary reports finding it using a Mestre-Nagao sieve over |a| <= 10^12, with a_p computed via quartic residue classes for primes p = 1 mod 4, followed by PARI/GP ellrank certification.\r\n\r\nApplied the degree-2 isogeny X = (x^2 + A)/x, Y = y*(x^2 - A)/x^2 with A = -248621438602. The resulting model is Y^2 = X^3 + 994485754408*X.\r\n\r\nNine supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 3956007662881795565721856. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:39:56",
  "updated_at": "2026-10-20 23:39:56"
}