{
  "id": 6391,
  "curve_key": "10126718573312942186141248:-31077604007268415607297801003498145280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-210973303610686295544609",
    "35969449082416267703539263137015391"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 172.73165869824624,
  "faltings_height": 12.31743518424119,
  "conductor": "122783327132041139329765184064",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "29",
    "31",
    "37",
    "103",
    "131",
    "241",
    "691",
    "4133",
    "24337"
  ],
  "discriminant": "42061263808872091731395544555978495743799205361567942482466440132952064",
  "regulator": "86353562.90453214861084637467281702531842410834191689552569",
  "points": [
    [
      "906841244151",
      "768375602493668928"
    ],
    [
      "14361772553985/529",
      "2116560235865803776528/12167"
    ],
    [
      "423090947253",
      "149814388538330340"
    ],
    [
      "328319262135",
      "45755267822136576"
    ],
    [
      "173648642478855/529",
      "555793032273821415552/12167"
    ],
    [
      "193656805426718631/237169",
      "-73786294961704598685920640/115501303"
    ],
    [
      "4848229160679/49",
      "-43472674873269291264/343"
    ],
    [
      "316556950266",
      "-30100136503907943"
    ],
    [
      "-39285743975615/81",
      "-113412422032147483696/729"
    ],
    [
      "5934649309572111/17161",
      "148579297168106347549248/2248091"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=-121/592. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [10,10]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:11:52",
  "updated_at": "2026-11-02 01:11:52"
}