{
  "id": 221,
  "curve_key": "85026209906584393825:-797096715342679514131865860625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1771379373053841538",
    "922565642019656180361670031"
  ],
  "rank_lower_bound": 14,
  "naive_height": 137.70154706301042,
  "faltings_height": 9.361977051261617,
  "conductor": "1067108442606429289452124323915075023850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "31",
    "43",
    "13921",
    "13030973",
    "225715883",
    "47972031521"
  ],
  "discriminant": "-11961746928396976832774801995263862052981467695744000000",
  "regulator": "24502377124.0149976223379472061761656606064202568292589204243053485",
  "points": [
    [
      "-993905311",
      "41247580093347"
    ],
    [
      "-618959415",
      "42212245856707"
    ],
    [
      "-135133735",
      "34051074286467"
    ],
    [
      "523368265",
      "11782775553267"
    ],
    [
      "546935705",
      "10832299311747"
    ],
    [
      "598100585",
      "8777953744707"
    ],
    [
      "609494201",
      "8326581312963"
    ],
    [
      "687993765",
      "5432840767267"
    ],
    [
      "772324505",
      "3893973423747"
    ],
    [
      "794554505",
      "4089081687747"
    ],
    [
      "827810585",
      "4844491588707"
    ],
    [
      "919786469",
      "8450622415863"
    ],
    [
      "3291849305",
      "175391699574147"
    ],
    [
      "9056167865",
      "852998874939267"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Specialization at T = -309/2 of the Mestre/Fermigier family y^2 = r(x,T) on the sextuple (a) = (-44, -60, -6, 110, 94, -94) [r = degree-<=4 remainder in p6(x-T)p6(x+T) = g^2-r, g monic degree 6, p6(x)=prod(x-a_i)]. Located by a Mestre-Nagao sieve of this family. Fourteen independent rational points were obtained via 2-descent covers; rank >= 14 follows from the positive-definiteness of their 14x14 Neron-Tate height-pairing matrix, verified independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the rank (no exact-rank/Selmer/BSD claim).",
  "created_at": "2026-06-25 22:06:57",
  "updated_at": "2026-07-01 22:43:39"
}