{
  "id": 218,
  "curve_key": "37168047451033625161:-159335239524567280443702326341",
  "ainvs": [
    "1",
    "0",
    "1",
    "-774334321896533858",
    "184415786422239825540685056"
  ],
  "rank_lower_bound": 15,
  "naive_height": 135.18594337975105,
  "faltings_height": 9.293392679912326,
  "conductor": "13737286227434328030396852859772916879098470",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "127",
    "151",
    "128983",
    "596538014056881445633451959507"
  ],
  "discriminant": "15022333163587070509998639856259499737597891168610762500",
  "regulator": "1779978689411.8084114367753707899730103398541064027289010096742171086",
  "points": [
    [
      "979729130622811281/166926400",
      "-959240687447310035515063389/2156689088000"
    ],
    [
      "10219787479/4",
      "-976013371455203/8"
    ],
    [
      "4528339940910/3481",
      "7625308316765958588/205379"
    ],
    [
      "391446893015/11449",
      "15397599381839218531/1225043"
    ],
    [
      "54547127865/64",
      "-6135098080565721/512"
    ],
    [
      "1269739826015/14884",
      "-19806885383250721019/1815848"
    ],
    [
      "23849164131/25",
      "2214544291703631/125"
    ],
    [
      "-438537424",
      "20968123525679"
    ],
    [
      "7914992168785/1089",
      "-22109430657093676121/35937"
    ],
    [
      "4642634492777710/208849",
      "316088285805959912636756/95443993"
    ],
    [
      "2450475884560/3249",
      "1004729461991195431/185193"
    ],
    [
      "110589032755840/22201",
      "1145551647025539063808/3307949"
    ],
    [
      "179225324275/169",
      "51800960300555549/2197"
    ],
    [
      "3796926254535/289",
      "7382233305884976321/4913"
    ],
    [
      "12459533075735/3844",
      "42451145483808864851/238328"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Specialization at T = -490 of the Mestre/Fermigier family y^2 = r(x,T) on the sextuple (a) = (1608, -870, -1080, -642, 1542, -558) [r = degree-<=4 remainder in p6(x-T)p6(x+T) = g^2-r, g monic degree 6, p6(x)=prod(x-a_i)]. Located by a Mestre-Nagao sieve of this family. Fifteen independent rational points were obtained from the low-height Mestre quartic cover together with 2-descent covers; rank >= 15 follows from the positive-definiteness of their 15x15 Neron-Tate height-pairing matrix, verified independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the rank (no exact-rank/Selmer/BSD claim).",
  "created_at": "2026-06-25 21:53:09",
  "updated_at": "2026-07-01 22:41:39"
}