{
  "id": 5563,
  "curve_key": "52529102529345797977357293327681:-387561564865821840911228372823614464561987663329",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1094356302694704124528276944327",
    "448566626002108885754849253332992317904869951"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 219.15240779595783,
  "faltings_height": 16.152894750365203,
  "conductor": "183703037667743189096443031268567527759721240246971898230542010",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "23",
    "31",
    "41",
    "47",
    "179",
    "57921001",
    "4272950013921049",
    "2269219725843894232757993657"
  ],
  "discriminant": "-3044020023904346226922533724854259690113824538262955401152408082596249436084996029440000000",
  "regulator": "269027752965232644.337681113719874017892698972607214656296437902813137917893466",
  "points": [
    [
      "520559332931659/9",
      "-530096467694260765426502/27"
    ],
    [
      "-1159040926963549",
      "-12646847068969273275826"
    ],
    [
      "569179037388251",
      "3174258490104286205774"
    ],
    [
      "123479810827219",
      "-17757208344656139708066"
    ],
    [
      "641480815429251",
      "3244362795421321673774"
    ],
    [
      "6920671433155291/9",
      "-212149280289931655129798/27"
    ],
    [
      "-924708105710109",
      "-25880931985739148726706"
    ],
    [
      "72473494183962851",
      "-19508496927147038901589426"
    ],
    [
      "506441606778782941/841",
      "68680252307591553290887536/24389"
    ],
    [
      "360240452692491",
      "10054091851293045542094"
    ],
    [
      "494457653252451",
      "-5323807423730233192626"
    ],
    [
      "1204337026496709",
      "-29620881105742568895264"
    ],
    [
      "1080264197050531",
      "-22956685794635823281586"
    ],
    [
      "19190194176177451",
      "-2654523834603167872792626"
    ],
    [
      "540720470103051",
      "3862755232377995885774"
    ],
    [
      "758189159592851",
      "-7394808477845584483426"
    ],
    [
      "253945908781351",
      "-13676107656744095037926"
    ],
    [
      "2016024192186851",
      "80225636503688557354574"
    ],
    [
      "503564203386531",
      "-5017989824430754112946"
    ],
    [
      "236117547869581",
      "14259516210942792147354"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 23/25 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -129423262682594003679387T^8 + 364444960853480119379208T^7 + 145088936906457036995136T^6 - 946405361864597551050816T^5 + 1086632441482958356509720T^4 - 615454597853371985855184T^3 - 2089672621773109442565264T^2 + 1503858169634937349756032T - 268043453574349038086592,\nA6 = 22378678518203765279639595291703734T^12 - 97642937907003790975195419097186584T^11 - 57701568157490976356217548246274864T^10 + 692728062356311676289756774010506240T^9 - 165059119295086271477298303488050440T^8 - 2065127205357525454766777049159397680T^7 + 866901377553305534044230525750471600T^6 + 2900595200522009433908965902519647040T^5 - 1511852767062133534934112666639840240T^4 - 1121738997234616988726901721424515200T^3 + 1300199883149489416130125996732379520T^2 - 448873241175573293059242892011302400T + 53141649442568035635166156713288960.\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": "2026-10-23 07:44:13",
  "updated_at": "2026-10-23 07:44:13"
}