{
  "id": 4200,
  "curve_key": "75492216627974499334800:-21810210219652094500197958420881600",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1572754513082802069475",
    "25243298865338072338192081505650"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 158.13537257530498,
  "faltings_height": 11.11573249285927,
  "conductor": "76711644195431677443287364353709744687885843783919989200",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "23",
    "11525771",
    "91657416306312217",
    "14643574507469001823127587"
  ],
  "discriminant": "-26301783914053199345599188151553303838258792560479997449051520000",
  "regulator": "14769618606876138.398917328686155972762160818107426084435264955963744503081",
  "points": [
    [
      "-3457338932283950/152881",
      "419479869614425008197270/59776471"
    ],
    [
      "704160568319525/49",
      "18685550649395726586160/343"
    ],
    [
      "-21983369718415/961",
      "209069066633909594420/29791"
    ],
    [
      "164310673150/9",
      "43662059186593240/27"
    ],
    [
      "62082601555",
      "12918375976212470"
    ],
    [
      "1954647280909/121",
      "2679362766332908048/1331"
    ],
    [
      "13463416501867325/351649",
      "959014804308362629051840/208527857"
    ],
    [
      "7682274653570475/477481",
      "668389601011663290428270/329939371"
    ],
    [
      "5433282443065/144",
      "7653492365140681235/1728"
    ],
    [
      "14841196475",
      "2273912615018870"
    ],
    [
      "-35601074725",
      "-6009404920280630"
    ],
    [
      "271939079745/64",
      "2210352288610426015/512"
    ],
    [
      "2296005900475/729",
      "88728873290807077790/19683"
    ],
    [
      "860305647425",
      "797123958533984620"
    ],
    [
      "1124260375303576725/30880249",
      "691548770821697914177542160/171601543693"
    ],
    [
      "-43485562475",
      "3377050417626880"
    ],
    [
      "28709623218267117525/2087667481",
      "237810201980439537133814187520/95387614874371"
    ],
    [
      "-14281079228247895/326041",
      "591540601510033950040420/186169411"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre rank-12 quartic family on locus sextuple [0,7,1182,1375,1382,1532] at T=391 (y^2=(g^2-p(x-T)p(x+T))/T^2, Jacobian); 18 independent points from a quartic rational-point search.",
  "created_at": "2026-10-12 15:12:38",
  "updated_at": "2026-10-12 15:12:38"
}