{
  "id": 4913,
  "curve_key": "58276599742652359208374080:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1214095827971924150174460",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 177.98172860404048,
  "faltings_height": 12.900051128644865,
  "conductor": "327561928777518231048733993255374727655208064800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "103",
    "151",
    "181",
    "631",
    "661",
    "977",
    "4019"
  ],
  "discriminant": "114535172485791776156914418331014446385389695512120022539696405467682304000",
  "regulator": "13093894653548632.775873807776044418759680877962161207598333420",
  "points": [
    [
      "41055940915081/36",
      "-67847460959150373691/216"
    ],
    [
      "241856990269504/121",
      "-3138188907918464236432/1331"
    ],
    [
      "650672909740681/16",
      "16591460504844377260709/64"
    ],
    [
      "789973375226327296/52441",
      "700251070498650130546438624/12008989"
    ],
    [
      "6260598355867249/2304",
      "-452808608306795050214647/110592"
    ],
    [
      "5369431969382464/2809",
      "321507282583239706877552/148877"
    ],
    [
      "503970756199849/4",
      "11313354507525137084597/8"
    ],
    [
      "819496426415104/729",
      "4647266315847933426368/19683"
    ],
    [
      "783572666247424/9",
      "21932297776307787698528/27"
    ],
    [
      "1375704900437598784/1185921",
      "504552281678913168979049008/1291467969"
    ],
    [
      "50328302790807616/15625",
      "-10609460671707747849364336/1953125"
    ],
    [
      "16156532404511231329/8928144",
      "51515091350968911844081233007/26677294272"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4767, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4767.\r\n\r\nThe source commentary identifies #4767 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 = 303523956992981037543615, giving y^2 = x^3 - 1214095827971924150174460*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 327561928777518231048733993255374727655208064800. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:47:34",
  "updated_at": "2026-10-20 22:47:34"
}