{
  "id": 345,
  "curve_key": "23278002649344714036283440529:-3235230694349377376079045989437788046430233",
  "ainvs": [
    "1",
    "0",
    "0",
    "-484958388528014875755905011",
    "3744479970311738957262814782831867617210"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 195.95191899951678,
  "faltings_height": 14.297350423023815,
  "conductor": "15587568597617774467402317716515315920379328015617095707375221511102745",
  "bad_primes": [
    "3",
    "5",
    "13",
    "17",
    "43",
    "59",
    "4957",
    "112680298688013869",
    "556778714430176039",
    "350570948823095172152501"
  ],
  "discriminant": "1242376586837912826623415817268660517325818940797865667216548646753671619520376575",
  "regulator": "1791167772689157304223.611019527105214873682087862686091484303980899842195464",
  "points": [
    [
      "-101791341984043097/6241",
      "-42169668028186974383448836/493039"
    ],
    [
      "3591783271004041/2209",
      "-5648818149132898530244360/103823"
    ],
    [
      "22664766398921638",
      "-3412138628304175859626214"
    ],
    [
      "7838223611066374/1089",
      "-899723019021596131359190/35937"
    ],
    [
      "2704011059006677/144",
      "61318917500151209301353/1728"
    ],
    [
      "7509774080558",
      "22936398763978883726"
    ],
    [
      "3255660216531480652013/49014001",
      "-176509781229836808564333129687464/343147021001"
    ],
    [
      "1934273239604399785979/37662769",
      "-78143223537438053882304294322460/231136413353"
    ],
    [
      "27097107906727960241/5161984",
      "429862079163436833922174015865/11728027648"
    ],
    [
      "53157468617172969089/3385600",
      "-5547766048575169911065244343/6229504000"
    ],
    [
      "34889287938698114918/3682561",
      "-3855530418535743739341789626/7066834559"
    ],
    [
      "-49304657155409122/3481",
      "18105848993468105624759644/205379"
    ],
    [
      "1049443481558",
      "-56891997641493955774"
    ],
    [
      "360814935600809/49",
      "8208552641946584083640/343"
    ],
    [
      "-1364906852124703/64",
      "33912365798984702720707/512"
    ],
    [
      "900834556517702/49",
      "11074555552417184584448/343"
    ],
    [
      "1815614187504105590/113569",
      "336802173476142362725524920/38272753"
    ],
    [
      "-43956697577661874/2209",
      "-7710433102642523745764222/103823"
    ],
    [
      "122103918760307/4",
      "1054842869711431238383/8"
    ]
  ],
  "submitter": "Christopher R. Hill",
  "commentary": "Found with Rank Hunter v0.7.21; family=Mestre/Fermigier sextuple, generic rank >=11; parameter=9736/9; local status: rigorous rank lower bound >= 19.",
  "created_at": "2026-08-25 01:51:19",
  "updated_at": "2026-08-25 02:23:48"
}