{
  "id": 200,
  "curve_key": "58267970912074998321:-479842416907924192177482963369",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1213916060668229132",
    "555373168020983867224329231"
  ],
  "rank_lower_bound": 13,
  "naive_height": 136.68651052546213,
  "faltings_height": 9.347716627138887,
  "conductor": "6177584096452092230279206747860870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "28755686340139143649765892789"
  ],
  "discriminant": "-18761498098102556371487217190377845102127324807168000000",
  "regulator": "12746195036.17266378810682497049084448405859392226472703342881533",
  "points": [
    [
      "14353961139/25",
      "862997361513753/125"
    ],
    [
      "52759158221/25",
      "10747244403736929/125"
    ],
    [
      "1986614540666021/638401",
      "83677707197040577478091/510082399"
    ],
    [
      "4289402483179541/1324801",
      "266593073543863450615179/1524845951"
    ],
    [
      "1225643375129621/323761",
      "41279856407830476915741/184220009"
    ],
    [
      "33314611142315909/8334769",
      "5872502213681351200460547/24062478103"
    ],
    [
      "4092206741",
      "253210335472629"
    ],
    [
      "1271021187149/289",
      "1392062438251856277/4913"
    ],
    [
      "59579399432021/11881",
      "449676106276783198641/1295029"
    ],
    [
      "1607845076494709/299209",
      "63218916112170048001407/163667323"
    ],
    [
      "5586961541",
      "410077035801429"
    ],
    [
      "6838692021",
      "558641128118069"
    ],
    [
      "341112840993869/5041",
      "6299253437563069859739/357911"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥13. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=2289/5: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 13 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.",
  "created_at": "2026-06-25 16:03:44",
  "updated_at": "2026-07-01 22:45:37"
}