{
  "id": 4279,
  "curve_key": "12603295788080828902745975117328475216:-46477929565478740479380206258606054920314009188519061440",
  "ainvs": [
    "0",
    "1",
    "0",
    "-262568662251683935473874481611009900",
    "53793899960044838430278277233936436925738609357115984"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 256.35714517719487,
  "faltings_height": 19.28791991255576,
  "conductor": "2102111046951998842720815252641704571627950736698543481130090482954333028675210882645528",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "193",
    "4337",
    "12659074067051",
    "77273938990273157139893910725586978609786919452643150244777"
  ],
  "discriminant": "-91580907476148768918937508710933634725319114574583338449936512532943814365576353536082185855487475177370368",
  "regulator": "3441781597093217147433951.1502169580128723106031593732078807390980199795896029766106014",
  "points": [
    [
      "-335703505699289974",
      "-322655225961629204796288906"
    ],
    [
      "2137604185946276510",
      "3043023374027517009944119578"
    ],
    [
      "136579392946298156",
      "143108958410493739825569156"
    ],
    [
      "402800389968850067",
      "115692524298079898745075456"
    ],
    [
      "1198745244530938166",
      "-1208977289696450037236151294"
    ],
    [
      "574203208338442640",
      "303885313257428081276043828"
    ],
    [
      "10790370982800500242/9",
      "32650744177361753239757581610/27"
    ],
    [
      "-546083168553650446",
      "185290307477435537177269458"
    ],
    [
      "4896741795549134156/25",
      "12424263168188794347358560396/125"
    ],
    [
      "-560216850941364016",
      "158332550999033611931958612"
    ],
    [
      "-19774660801978966",
      "-242854634637916392996703062"
    ],
    [
      "192940568988922256",
      "101568551600355459162270156"
    ],
    [
      "-58883967640134810151/256",
      "1308281263588305599380697142243/4096"
    ],
    [
      "5954706253981476914480/24649",
      "-258484082900819897354308489833804/3869893"
    ],
    [
      "626147461610879879",
      "367253285120014727075392842"
    ],
    [
      "144103536555770210",
      "137656298711655063955193922"
    ],
    [
      "-233027161122264304",
      "-319883992656767154779391756"
    ],
    [
      "414698918699212880",
      "-127376945680067405679003372"
    ],
    [
      "57616847313121004",
      "197121262549109125536016092"
    ],
    [
      "626567418084303725546/1849",
      "4856135038792195392152618687694/79507"
    ],
    [
      "9320790938743823066/25",
      "10986406415846893234444788414/125"
    ],
    [
      "26171835115876629323/121",
      "-112313945888585997523469452380/1331"
    ],
    [
      "4443273580963927106/121",
      "-279831670568528050819764337014/1331"
    ],
    [
      "245607305290197836",
      "64194043161076025542947756"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 54/103 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": "2026-10-16 13:55:13",
  "updated_at": "2026-10-16 13:55:13"
}