{
  "id": 4916,
  "curve_key": "248120199369812856512010816:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5169170820204434510666892",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 182.32786660645027,
  "faltings_height": 13.262229295512347,
  "conductor": "5937850437433996936516077156029887017540129986592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "47",
    "67",
    "103",
    "127",
    "149",
    "353",
    "733",
    "2687"
  ],
  "discriminant": "8839803806185522806373912781989731104006643263104402253996144963598233874432",
  "regulator": "8043198251240090.6254460042389333823161456785097603217441708100",
  "points": [
    [
      "3079259867524",
      "-3644150549584600196"
    ],
    [
      "2334337845316",
      "-808409996580587932"
    ],
    [
      "209206891008196/49",
      "2561242523424976586852/343"
    ],
    [
      "59222043883396/25",
      "127968760707713132444/125"
    ],
    [
      "1363335547543876/289",
      "-44106813268514267578012/4913"
    ],
    [
      "13747041445937284/4225",
      "1153018599095667660072452/274625"
    ],
    [
      "48223427487481/16",
      "219838795584994334323/64"
    ],
    [
      "511555739289604/225",
      "912384988684218692/3375"
    ],
    [
      "26955878201462116/5041",
      "-4005722320570672136021908/357911"
    ],
    [
      "191676105741796",
      "-2653514174147099798548"
    ],
    [
      "528600960925899607201/106090000",
      "-10814222756680644391198267569551/1092727000000"
    ],
    [
      "1582040840365129/400",
      "51489433058250706477883/8000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4768, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4768.\r\n\r\nThe source commentary identifies #4768 as a 2-isogenous model of a curve listed in 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 = 1292292705051108627666723, giving y^2 = x^3 - 5169170820204434510666892*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nTwelve 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 5937850437433996936516077156029887017540129986592. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:50:06",
  "updated_at": "2026-10-20 22:50:06"
}