{
  "id": 4954,
  "curve_key": "-122115510204332724048043200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "2544073129256931751000900",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 180.20102890082043,
  "faltings_height": 13.084992820043192,
  "conductor": "20352585034055454008007200",
  "bad_primes": [
    "2",
    "5",
    "7",
    "17",
    "97",
    "173",
    "79873"
  ],
  "discriminant": "-1053825605659343585536882926939950003810100374823697666914998715566656000000",
  "regulator": "26391052108.88394106559122829475720259871369352848058",
  "points": [
    [
      "33255370962009/16",
      "241736257719465283677/64"
    ],
    [
      "91300399095074481/1254400",
      "605186002750844126673854871/1404928000"
    ],
    [
      "721524604114605340729/205119684",
      "21280407807456700850690318916467/2937724114248"
    ],
    [
      "3831601149809607321/7139584",
      "23518868291005270974345636669/19076968448"
    ],
    [
      "10076592065442177369241/1742400",
      "1011510819077737186904012494710211/2299968000"
    ],
    [
      "741805377325573669267229056955241/301869013388794437184",
      "24086690904399616272421101031823765004158411969589/5244786366838544479925271029248"
    ],
    [
      "290116319853020824085686488107116321/21817882436829177924",
      "156263750189218900803928627807052909035990484860352081/101910491448465399705496921032"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #2901, submitted by Natanael Wildner Fraga: https://elliptic-rank.icarm.cloud/curve/2901.\r\n\r\nThe source commentary attributes this rank >= 7 congruent-number curve, with d = 797507543735, to Watkins et al. (2014), Section 15 electronic data: https://doi.org/10.5802/pmb.9. The cited witness x-coordinates are at https://magma.maths.usyd.edu.au/~watkins/PTS.r6r7.\r\n\r\nThe source model is y^2 = x^3 - 636018282314232937750225*x. Applied the degree-2 isogeny X = (x^2 + A)/x, Y = y*(x^2 - A)/x^2 with A = -636018282314232937750225. The resulting model is Y^2 = X^3 + 2544073129256931751000900*X.\r\n\r\nSeven 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 20352585034055454008007200. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:45:08",
  "updated_at": "2026-10-20 23:45:08"
}