{
  "id": 4912,
  "curve_key": "34366601997282575734456896:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-715970874943386994467852",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 176.39738235738832,
  "faltings_height": 12.768022274757184,
  "conductor": "113914287503822021953053632003640671122813665312",
  "bad_primes": [
    "2",
    "3",
    "19",
    "43",
    "47",
    "67",
    "109",
    "127",
    "137",
    "233",
    "593",
    "29501"
  ],
  "discriminant": "23489081882687228749445503846959090657760592328797915470548586868606349312",
  "regulator": "6336990891876100.5699352939549948851811083155583091164254186468",
  "points": [
    [
      "1913778959236",
      "-2374679125501637572"
    ],
    [
      "39097182695076/25",
      "205592492556100061676/125"
    ],
    [
      "1479225213725809/64",
      "56853895105822532008951/512"
    ],
    [
      "5951487147489/4",
      "11942587547687947761/8"
    ],
    [
      "101309177040516/49",
      "-930395934915891056892/343"
    ],
    [
      "102398330070436/121",
      "17197950579233078548/1331"
    ],
    [
      "182833152739561/16",
      "-2465406338182294664843/64"
    ],
    [
      "127514368035076",
      "1439889359813244161668"
    ],
    [
      "5000004367282681/1296",
      "-344945708205131931257843/46656"
    ],
    [
      "101101375986724",
      "1016530441591110894476"
    ],
    [
      "266613413546601/196",
      "3408588081668994945237/2744"
    ],
    [
      "15906516982923681/4624",
      "1944510144272849821675023/314432"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4766, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4766.\r\n\r\nThe source commentary identifies #4766 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 = 178992718735846748616963, giving y^2 = x^3 - 715970874943386994467852*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 113914287503822021953053632003640671122813665312. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:46:25",
  "updated_at": "2026-10-20 22:46:25"
}