{
  "id": 4272,
  "curve_key": "338583072754762645211329053140101425:-212197996398864015753237098831334224508751020429635625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-7053814015724221775236021940418780",
    "245599532869055575551922368319173759212652499490847"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 245.57871905358093,
  "faltings_height": 18.421043927514678,
  "conductor": "10933472300508705020969962539660253800362336377452333549387041584971844109759650",
  "bad_primes": [
    "2",
    "5",
    "7",
    "17",
    "23",
    "29",
    "43",
    "71",
    "191",
    "1087",
    "8627",
    "1437607",
    "42526165861297369",
    "8240800266961743014968600626321223301"
  ],
  "discriminant": "-3595680007295395624750938366224957142376166944416579039580816499198390200959901134874968447581696000000",
  "regulator": "19760488592436140822249.3236065392911275978157971415471432058610225474608853392097006",
  "points": [
    [
      "693862462675865581/9",
      "-341546829692943720365030185/27"
    ],
    [
      "-89380448766701771",
      "-12728876185521812299879515"
    ],
    [
      "51870854084096229",
      "-4390346637698918682065515"
    ],
    [
      "-24953855568982491",
      "-20151445350974727353884155"
    ],
    [
      "33093484988699009",
      "6957551715676731406915345"
    ],
    [
      "-83447435193850091",
      "15910315523313294744467845"
    ],
    [
      "-46818918911689771",
      "21753709733674927632493285"
    ],
    [
      "2006031825841052919",
      "-2838784221617487582238158685"
    ],
    [
      "65293144503873909",
      "7961860546768649234662245"
    ],
    [
      "-68981667559012075",
      "-20098163041208602359848059"
    ],
    [
      "1378249379378273221/49",
      "2858374545467490833441286355/343"
    ],
    [
      "-52103707986155371",
      "-21718159205334573435621115"
    ],
    [
      "-22882925517906091",
      "19875343698327007334262245"
    ],
    [
      "-53815398240240371",
      "21664457673428005413011485"
    ],
    [
      "215544383950286629",
      "93483946590269046707868885"
    ],
    [
      "-11593079508880679411/121",
      "8617689674971585939220265695/1331"
    ],
    [
      "522514494554858869",
      "373118636011823724915241765"
    ],
    [
      "47656614590435369",
      "4204057068798243807426265"
    ],
    [
      "23298593599274525",
      "9690337101548445848677741"
    ],
    [
      "73313215004942479",
      "11068316594066765665459285"
    ],
    [
      "154137361938773759",
      "-53107334747958212758334155"
    ],
    [
      "1378424279795865862021/18769",
      "28595856732894822982259296227485/2571353"
    ],
    [
      "-93961332960265771",
      "-8878393082292608415762715"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 39/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9801785533668367408277499T^8 - 121843241966486333706286824T^7 - 383434732762042957835672232T^6 - 85754468638713501529031952T^5 - 584201627367901316547607440T^4 + 1235140044591109335942134016T^3 + 994771523582906627448194816T^2 - 550790635100880788122728032T - 647714191600162651688347312,\nA6 = 12142329458953725303990225302566830294T^12 + 247791101750863056653001398463488667192T^11 + 1886090538602583189200926091842195641480T^10 + 5912076790668428510577901681319655809040T^9 + 1282952245208814516295621371483268940160T^8 - 25791045529140834460411754210526102555072T^7 + 619130399100809058015628676691838434624T^6 + 31601519751505535243254509940106610677280T^5 + 10405299225003196422075679041028274690640T^4 - 27172444692997266799042742904489658895040T^3 - 13432438015701644454859263568215615214016T^2 + 8212424024664720375926323815936672405632T + 6370397708074310285430666560056789129600.\nIt is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-16 03:23:49",
  "updated_at": "2026-10-16 03:23:49"
}