{
  "id": 803,
  "curve_key": "42874128066111556265683663604935744161464476680254469184:-278483174801214459373819570490190904545581736074781079470907615763850814152802446848",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-893211001377324088868409658436161336697176597505301441",
    "322318489353257476127105984661383880720198001931577617014493148996108419252695905"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    4
  ],
  "naive_height": 384.293590770922,
  "faltings_height": 29.880098213034728,
  "conductor": "14545260576720879419495082714314736176851942086001467334920374959680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "37",
    "43",
    "47",
    "53",
    "59",
    "61",
    "617",
    "1117",
    "1277",
    "2309",
    "6173",
    "8521",
    "9811",
    "29753",
    "123953",
    "138433",
    "94669559"
  ],
  "discriminant": "727981240750541222694605443492506965011952771782563642424519939288105666673830161019217697907939220986042382042763173648900896710312090447323656092919412952268800",
  "regulator": "2959528483927425105.811682154886994510350220814218174837267225900",
  "points": [
    [
      "597612317292471058196192631",
      "1398622144944316533016655735316987556992"
    ],
    [
      "694353949816071705410997776",
      "6072970634448242529201207496469911518217"
    ],
    [
      "-598632869473801622467375497",
      "25347526376241932883206773405735436724960"
    ],
    [
      "-933661432500914851209854752",
      "18503523487265112186367665783433424344255"
    ],
    [
      "375160895678322358953429710645/484",
      "104153933807274778329809795564901718854558485/10648"
    ],
    [
      "683822993666349167197162774469/1156",
      "38111706823499015231331988739330510894730973/39304"
    ],
    [
      "3350076553193143356927710856431/841",
      "5972709618324560578026964149122537091878422112/24389"
    ],
    [
      "2659496632285762198527249864536/4225",
      "845757290666752961117122319549083532947519459/274625"
    ],
    [
      "8803469959946669150726776232351/13225",
      "7246709153189091176128601501137042920495475976/1520875"
    ],
    [
      "59922440315103684935670336679895/97969",
      "67274167788011522588362862411152926306556728680/30664297"
    ],
    [
      "39814735278556116776643405054777/258064",
      "1798384890398849925987320469589374484084700455845/131096512"
    ],
    [
      "-416171738076975399658856525095187/385641",
      "1299363047434402764524514232926677865112194116560/239483061"
    ],
    [
      "38292404270227662119661437613226054707331/65310884695225",
      "217293391098098252518162242915860479398832158981430051315404/527810894327731265875"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Found May 2026 without AI assistance. Specialization at T = 14121191/38310928 of the fibration 'E1' published in Elkies & Klagsbrun 2020, \"New rank records for elliptic curves having rational torsion.\"",
  "created_at": "2026-09-18 16:13:24",
  "updated_at": "2026-09-18 16:13:24"
}