{
  "id": 208,
  "curve_key": "14625378343497043567612061435329:-55953489917540816135135028393347911408859680417",
  "ainvs": [
    "1",
    "0",
    "0",
    "-304695382156188407658584613236",
    "64760983700857400691050362439563148137462416"
  ],
  "rank_lower_bound": 12,
  "naive_height": 215.28169998638668,
  "faltings_height": 15.6797000963728,
  "conductor": "1107988077126197589769596508555487707559725219449598542068453069615896859730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "31",
    "157",
    "4513",
    "11249219",
    "1500692293891444032300619619",
    "4330572287574020219420543749507"
  ],
  "discriminant": "-1388810570434782811007607331048073936871115674258540673227450623892810201037842324019200",
  "regulator": "147652040099442.05947295954239201960603808166881615690156257635",
  "points": [
    [
      "44278949867297760957064/935089",
      "-9316796137756519793643768214532204/904231063"
    ],
    [
      "158955475956867724/9",
      "-63343723260583635566586476/27"
    ],
    [
      "7690985079964216766320/5368489",
      "-630406900594136415745523463507692/12438789013"
    ],
    [
      "77834314090789836/361",
      "20678751759625129232805588/6859"
    ],
    [
      "299913011917936",
      "596149116860699711812"
    ],
    [
      "53714858859344400/169",
      "350978976489095631299388/2197"
    ],
    [
      "47471468885246317/144",
      "649332284048410916301671/1728"
    ],
    [
      "399524613364744",
      "2607635597175266655628"
    ],
    [
      "656000246676580",
      "12131836808507316807904"
    ],
    [
      "15043833852323541/16",
      "1580027181914339609144013/64"
    ],
    [
      "101292582467515835873416/80263681",
      "29562434295869282672212131124865908/719082318079"
    ],
    [
      "1139227591149379/4",
      "8328224915694189545111/8"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥12. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=967/9: 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 12 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 16:04:24",
  "updated_at": "2026-07-01 22:47:35"
}