{
  "id": 6423,
  "curve_key": "2151639629224520241008448:-2809794003161013897918513457625372160",
  "ainvs": [
    "0",
    "0",
    "0",
    "-44825825608844171687676",
    "3252076392547469789257538724103440"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 168.08481720478528,
  "faltings_height": 11.985562073284656,
  "conductor": "5763174267608696604990665002229568",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "47",
    "79",
    "109",
    "199",
    "239",
    "317",
    "337",
    "587",
    "877"
  ],
  "discriminant": "1195710394997773314358395846806197782372683163118199542934795044798464",
  "regulator": "69649204.74332628648093086353912299048473447274353491155066",
  "points": [
    [
      "313382641632",
      "-141355354845155724"
    ],
    [
      "6577188726798/169",
      "86954567664778905168/2197"
    ],
    [
      "7980768303229/9",
      "-21947889206253885875/27"
    ],
    [
      "2516280408006",
      "3977776713509533440"
    ],
    [
      "5432848970577/64",
      "3919263908220474201/512"
    ],
    [
      "12835874000406/25",
      "-42497485704478262304/125"
    ],
    [
      "156795287904",
      "-8852855186286540"
    ],
    [
      "-11717095113090/49",
      "-5918898579193584720/343"
    ],
    [
      "602618851804",
      "-441678516383784680"
    ],
    [
      "191290498927065/16",
      "-2645284604194258481565/64"
    ]
  ],
  "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=3476/2219. 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 16:05:42",
  "updated_at": "2026-11-02 16:05:42"
}