{
  "id": 202,
  "curve_key": "369566474541430613329:-7136960510098350839243221718617",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7699301552946471111",
    "8260370960120371675267448841"
  ],
  "rank_lower_bound": 13,
  "naive_height": 142.0856795533432,
  "faltings_height": 9.672248385828121,
  "conductor": "377567090887779694323895274233922490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "137",
    "91773698536932579421526229059"
  ],
  "discriminant": "-266808849431496166419387240071765982358706830625053900800",
  "regulator": "6519710445.716869994962627499550559448523343955253137275995743738",
  "points": [
    [
      "38654232246",
      "-7580643190350363"
    ],
    [
      "203345746649964702/22819729",
      "87698553847271448902404101/109009845433"
    ],
    [
      "6220241216550/49",
      "15509840583005224947/343"
    ],
    [
      "110996977707102/82369",
      "430829851308717157515/23639903"
    ],
    [
      "3833518434406794/2122849",
      "48470044901113166359581/3092990993"
    ],
    [
      "9919516408158",
      "-31241782325935811763"
    ],
    [
      "143201575382181750/1229881",
      "-54175148608867446972558159/1363938029"
    ],
    [
      "1006894711087356/32041",
      "-31829950172644810031097/5735339"
    ],
    [
      "11127316314114/625",
      "-36692149724825773563/15625"
    ],
    [
      "1893419200260/169",
      "-2532103404406521687/2197"
    ],
    [
      "51182275986198/6241",
      "-347474912239071226197/493039"
    ],
    [
      "370092489225438/72361",
      "-6237092781954126380967/19465109"
    ],
    [
      "4632706890",
      "-268365492663219"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥13. Mestre–Fermigier construction from the integer 6-tuple a=[-72, 120, 144, -48, -24, -120] with shift t=1516/7: 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 16:03:54",
  "updated_at": "2026-07-01 22:45:38"
}