{
  "id": 5719,
  "curve_key": "149365858708812662739891027696:-57381367684725078441434136487354007980607256",
  "ainvs": [
    "0",
    "0",
    "1",
    "-3111788723100263807081063077",
    "66413620005468840788696917230733805533110"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 201.52858870417185,
  "faltings_height": 14.63733909894557,
  "conductor": "19151951012034005307958308679165188198546454669246688318105",
  "bad_primes": [
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "1877",
    "878279608068556917961",
    "17409276861678186854864603"
  ],
  "discriminant": "23006256536144482605156151897508805801578325555982594831785211061983176178945703125",
  "regulator": "25036057788520844.64824033146789810538280299031334053175092082428563084733170",
  "points": [
    [
      "63315850559478",
      "351019642328299274687"
    ],
    [
      "46734389127228",
      "151851244229483361062"
    ],
    [
      "35315510319853",
      "-23752841621852338938"
    ],
    [
      "-57413973190772",
      "-236254950792616192938"
    ],
    [
      "30149734898228",
      "566017341226614062"
    ],
    [
      "29808936940728",
      "11912783437599821562"
    ],
    [
      "111671245723337/4",
      "-288283035168314315679/8"
    ],
    [
      "36836567312620",
      "-42080252719588110346"
    ],
    [
      "6266670335728",
      "-217161611060958626563"
    ],
    [
      "35659393695728",
      "28166174244043773437"
    ],
    [
      "63776515068068",
      "-356878095645014501058"
    ],
    [
      "26418162946978",
      "-51416195290044272188"
    ],
    [
      "-57374426797522",
      "236820924755397533687"
    ],
    [
      "1702400497894353",
      "70204064139583981078062"
    ],
    [
      "64258200940785",
      "-363022403618036770066"
    ],
    [
      "-49384332421622",
      "315670891835728316387"
    ],
    [
      "8382802510703",
      "-202279956416985957738"
    ],
    [
      "54293323789793",
      "-239808730742034972018"
    ],
    [
      "82260695550250008/2401",
      "481450124298515661367098/117649"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 8/13 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -213546515196627504820332T^8 + 869465515207593907398960T^7 - 510065089965030971860884T^6 - 1270257582515056045578720T^5 + 1426065508735989008931900T^4 - 690890144029437273227280T^3 - 1389292332816820391566956T^2 + 1307996517837724132656960T - 286267614586960854758400,\nA6 = 38855172470975738993518813988244756T^12 - 243637332934783116837818686074203520T^11 + 382613702852074064448992630465758608T^10 + 438404888400781537256687728554749760T^9 - 1340270054837389026155362835012033304T^8 - 438466811942831565597983911599431040T^7 + 1981768199902501016022471226901183040T^6 + 697917175039489822346233336938891840T^5 - 1626320407404938608434545478196300764T^4 - 187748176254897658526766053163492480T^3 + 919892555571017546557734659258394000T^2 - 417938005135807422838969764298752000T + 59851413200989840657350337781760000.\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": "2026-10-24 16:36:29",
  "updated_at": "2026-10-24 16:36:29"
}