{
  "id": 5979,
  "curve_key": "2557309150911932114507868749181390081:-4381608851934858779658085225411257271359485316959515521",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-53277273977331919052247265607945627",
    "5071306541591271749034694912633046049357517000319179"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 251.634021992831,
  "faltings_height": 18.922199720407345,
  "conductor": "175363906724941939917345509202231003059281386917758326349323466305344130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "83",
    "107",
    "131",
    "197",
    "1704979069",
    "2794911869439479530045299668088511856914879"
  ],
  "discriminant": "-1431787493201184053584244540330170275725781799953750242511415787925919593827345043463445607727380480000000",
  "regulator": "65513038297862832884.88498139782941564370784031589718164847190093171257498182581112",
  "points": [
    [
      "206897969748634187",
      "-53897871145559874719641094"
    ],
    [
      "-217180536364445813",
      "79989095773272193240286906"
    ],
    [
      "3070382155266954187",
      "-5365327520510661044099841094"
    ],
    [
      "483520293044461787",
      "-303897645411620862472225094"
    ],
    [
      "146819192887658027",
      "20346901539037755388414906"
    ],
    [
      "1114606684822080187",
      "-1153437279056312400107169094"
    ],
    [
      "172575527524074187",
      "-31884968410479180760041094"
    ],
    [
      "196310888065251787",
      "-46667115524483382099426694"
    ],
    [
      "76077215022001307",
      "38189465199978505273742506"
    ],
    [
      "-267953836896061943",
      "-10405270946601873859719994"
    ],
    [
      "-57937741836924563",
      "-89238932742834149718115594"
    ],
    [
      "7544003790973387",
      "68336022188231471502590906"
    ],
    [
      "164770414487977867",
      "-27680095963128032706971974"
    ],
    [
      "1278322877293253779/25",
      "-6225922445845527086554031918/125"
    ],
    [
      "124797132275787787",
      "19133387877792112546277306"
    ],
    [
      "189661375787021707",
      "42297254894091423301145786"
    ],
    [
      "116064153531926987",
      "21241751687520230741246906"
    ],
    [
      "-134669826896840693",
      "-99014043912700181006751814"
    ],
    [
      "143506532282986987",
      "19520787314947780182166106"
    ],
    [
      "-242730165861345503",
      "-60845281862773129311295354"
    ],
    [
      "200092548274146187",
      "49214143793423376372158906"
    ],
    [
      "3203839701838889779/25",
      "2332993447036899749018130898/125"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -337/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -11871310334515632T^8 + 4710110008611306816T^7 - 2086020069231986711136T^6 - 184523251173755635536480T^5 - 6701046568565117730395760T^4 - 153188863150147099034594256T^3 - 1728397061227994797149412104T^2 + 1293824158270290221749735140T - 3009001448051781638619102975,\nA6 = 425207191402126274866560T^12 - 563052339092973212554731264T^11 + 242123500866097746692387835264T^10 + 23032729293888429602372703530880T^9 + 3121622944690084624163225355490944T^8 + 295262495155831884321522320323442496T^7 + 13000284347332506536750445881902721952T^6 + 266703534992086688942874014282698665168T^5 + 2231811615310432924685764525429401885924T^4 + 6596027232624269118843692038876188450360T^3 + 95451184990094031890361698435840315288700T^2 - 68941255711464655644860348072488527433500T + 38303805195121251570249945560744186021250.\nIt is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration 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": "2026-10-27 15:48:03",
  "updated_at": "2026-10-27 15:48:03"
}