{
  "id": 4917,
  "curve_key": "-292990248513394159101179345280:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "6103963510695711647941236360",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 203.54981051333462,
  "faltings_height": 15.030724621086042,
  "conductor": "149033482159618868502058245714126232025398782901544198400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31",
    "67",
    "89",
    "307",
    "317",
    "337",
    "1223",
    "2153",
    "10657"
  ],
  "discriminant": "-14555118991587742373051858942360454073739663548506909087714094641261415431698141184000",
  "regulator": "2143188679959624727.208417489912078208017205811128407134080090183",
  "points": [
    [
      "70666199129761/25",
      "16429936844221620877741/125"
    ],
    [
      "3852288531175249/4",
      "239884719025062710481817/8"
    ],
    [
      "1850760618334010161/76729",
      "8535137139960794827843781371/21253933"
    ],
    [
      "525361621651445569/121104",
      "6868502824552041304132600607/42144192"
    ],
    [
      "28181810869748909569/49284",
      "-150997434338290516124340380993/10941048"
    ],
    [
      "925246452299387761/3721",
      "-932889411841948625690287771/226981"
    ],
    [
      "48050866213379450521/470596",
      "-419402569274684175696610648189/322828856"
    ],
    [
      "6462471871029001/324",
      "2100202778453363782333019/5832"
    ],
    [
      "421903082123050603391449/11873589156",
      "661942790166104232875791500365090083/1293817515972696"
    ],
    [
      "2256475331470677166201/4137156",
      "108282036692345010576664681209331/8414975304"
    ],
    [
      "201697482782990041/225",
      "90927217426347269629029161/3375"
    ],
    [
      "24900019762354801/400",
      "-6305275226808462194440951/8000"
    ],
    [
      "2080554156623651739772222009/25797297442816",
      "-132127646679682537253682759085210614444013/131027156630996516864"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4772, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4772.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 1525990877673927911985309090*x to Aguirre, Castañeda and Peral, High rank elliptic curves with torsion group Z/(2Z), Mathematics of Computation 73 (2004), 323–331: https://doi.org/10.1090/S0025-5718-03-01547-3.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -1525990877673927911985309090, giving y^2 = x^3 + 6103963510695711647941236360*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nThirteen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 149033482159618868502058245714126232025398782901544198400. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:51:16",
  "updated_at": "2026-10-20 22:51:16"
}