{
  "id": 5692,
  "curve_key": "24620850899884724119426838995776:-122046639690301286956929479425860260718506798976",
  "ainvs": [
    "0",
    "0",
    "0",
    "-512934393747598419154725812412",
    "141257684826737600644594304891041968424197684"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 216.84343941392405,
  "faltings_height": 15.843228428379957,
  "conductor": "57578227304047373592559760860388964753492018986548896974399690484840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "43",
    "311",
    "24967",
    "13694806471",
    "34943838246788200124719748695571928665263229"
  ],
  "discriminant": "17037168046036058290571260473842969340119655341326726959051214853649141809644348884000000",
  "regulator": "23860263390399418025.518780012079495589055668548158510369220190716906290639610450",
  "points": [
    [
      "380713120902273",
      "1076259745465970390325"
    ],
    [
      "424644396055038",
      "126737028326211333030"
    ],
    [
      "-206967412800990",
      "15445155698942381670258"
    ],
    [
      "143246177143228",
      "8409585545079276547990"
    ],
    [
      "376368741383508",
      "1232532194175112017330"
    ],
    [
      "492149897848698",
      "-2832216645573889254450"
    ],
    [
      "431180096786598",
      "503965382843494722150"
    ],
    [
      "-609991379432562",
      "15072221675342915110170"
    ],
    [
      "1228394029902198",
      "-36942653318585589625050"
    ],
    [
      "424841653995918",
      "147111588054437716710"
    ],
    [
      "537107815633548",
      "-4550171076431690960250"
    ],
    [
      "402841817880804",
      "6916907771349159870"
    ],
    [
      "1397993799383817/4",
      "17304526412121356533125/8"
    ],
    [
      "7403090815772193/16",
      "110520016812998567549775/64"
    ],
    [
      "37505111529548092/9",
      "7162448496414542364343310/27"
    ],
    [
      "773296639504548",
      "14388506352691860138750"
    ],
    [
      "776514775855978",
      "-14531885599515829534990"
    ],
    [
      "13752990895803318",
      "1610711960090258151216090"
    ],
    [
      "426129516518865",
      "245986732425134623923"
    ],
    [
      "1652542869407358",
      "-61697143531183767390630"
    ],
    [
      "79361805721190964/25",
      "-21831380773801389463735062/125"
    ]
  ],
  "submitter": "Nikita-Shulga",
  "history": [],
  "commentary": "Specialization T = -106/7 of the elliptic-surface construction associated with curve#3792. Found and verified in an AI-assisted computational search. These 21 rational points certify a rank lower bound of 21, not an exact-rank claim. All primes dividing the minimal discriminant are supplied for conductor computation.",
  "created_at": "2026-10-24 12:57:42",
  "updated_at": "2026-10-24 12:57:42"
}