{
  "id": 6412,
  "curve_key": "21819123301187813710412637768516129:-3223147930671759177975571707475583555370468888186033",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-454565068774746118966929953510753",
    "3730495290129351014075956669931418116003864405681"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 237.20439648583243,
  "faltings_height": 17.44481065885421,
  "conductor": "1150660788551932761609211252461298678005146490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "29",
    "37",
    "41",
    "43",
    "97",
    "163",
    "251",
    "439",
    "5059",
    "430695673",
    "137984182321"
  ],
  "discriminant": "-672561463165385061573214110956584844728149154838205576635959389750038925681196095930421267660800",
  "regulator": "588965431846153.92307235701788265879300510592999662202582730354",
  "points": [
    [
      "102766819397589704748951/21025",
      "32943918008362314932878355110500964/3048625"
    ],
    [
      "60443533066876885129575/4977361",
      "387597987166535806663339884930812/11104492391"
    ],
    [
      "-129958177918318623895905/25421764",
      "311884713517233589225177805193295451/128176534088"
    ],
    [
      "291921529723116260522719212710175/23723352221729161",
      "52864561504682304774769127354090657151021875828/3653962494840471247343909"
    ],
    [
      "1258229409355986100718374543/50368376041",
      "31900391318058511379867821613643553842164/11304124266505589"
    ],
    [
      "1970887453253280163375/170569",
      "-10161804230499914866389919240396/70444997"
    ],
    [
      "1323966071328966095855889523335/20648454019249",
      "1448105268661577736795955944982372401854804036/93827752025346553193"
    ],
    [
      "212733839697372761989240204063/15047734897881",
      "-21021678205563614650932913194836993254049900/58372285399501000221"
    ],
    [
      "68959874707378162055899575/5417107201",
      "-32916591445638906658214632394733065308/398704507100801"
    ],
    [
      "79012804815496795552826684655/2917602193801",
      "-16738974338281064826977382265047483551731892/4983553389629294299"
    ],
    [
      "197154807105867415423/19321",
      "-1055779117833044331563396362836/2685619"
    ],
    [
      "1595120506608547016375503/131308681",
      "51427578469002659537621272714798124/1504666175579"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), t = 3507/601 for E = [A, 0, B, 0, 0], where A = 13*t^2 + 3711, B = -1189*(t^2-25)*(t^2-121)*(t^2-361), own construction similar to https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-11-02 11:59:28",
  "updated_at": "2026-11-02 11:59:28"
}