{
  "id": 196,
  "curve_key": "28083791162533682241:-155024078761605995745679880289",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-585078982552785047",
    "179426017231461870343844271"
  ],
  "rank_lower_bound": 14,
  "naive_height": 134.42675592508496,
  "faltings_height": 9.130304325350192,
  "conductor": "15241162564541931655288262509967985228690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "5693",
    "134599091459570158754656517308997"
  ],
  "discriminant": "-1089582079144626137486468331565725618132214569984000000",
  "regulator": "418268198207.917346994581019827048869512072621751054302130902941757",
  "points": [
    [
      "745371953239691/2088025",
      "12089821218503314681926/3017196125"
    ],
    [
      "7029737347501871/18653761",
      "284338310384923385718546/80565593759"
    ],
    [
      "840199390735491/1985281",
      "7718166572582854963326/2797260929"
    ],
    [
      "15489085411221/32761",
      "17275921179556260504/5929741"
    ],
    [
      "23487639989/49",
      "1035223960079142/343"
    ],
    [
      "82305778619/169",
      "6945576670507158/2197"
    ],
    [
      "384190709219/289",
      "205579825992367902/4913"
    ],
    [
      "84104283089/49",
      "22312839290733942/343"
    ],
    [
      "229101138094731/96721",
      "3306517985548651348914/30080231"
    ],
    [
      "3176482211",
      "-174276552517506"
    ],
    [
      "-30900100109/81",
      "13581992367211726/729"
    ],
    [
      "-2023912553071/6889",
      "10323306496153093428/571787"
    ],
    [
      "151595411",
      "9706343114094"
    ],
    [
      "1191988196819/5329",
      "3006911455148593998/389017"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥14. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=267/2: 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 14 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 16:03:24",
  "updated_at": "2026-07-01 22:43:38"
}