{
  "id": 5967,
  "curve_key": "22962790507482529308729663964051495434811456:-109796032659105780885750479874199967816585426852480904204134912896",
  "ainvs": [
    "0",
    "1",
    "0",
    "-478391468905886027265201332584406154891905",
    "127078741503594653802792480475873926667515102857287725962414403"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 299.52734702279554,
  "faltings_height": 22.763430670941887,
  "conductor": "11453057263688698098742535669886806309000076820212260831211775517718624305960064358248066360",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "29",
    "53",
    "79",
    "157",
    "167",
    "192097",
    "2488949",
    "18563242045751583918041",
    "3273531681496498421689375926154260842497"
  ],
  "discriminant": "30599091362320288357785145810551400413454704352254194539198511337599465135423117091178600195992340627097818074409846932000000",
  "regulator": "39304166203777634089884255.93686422827581722250500862028147980950404414159020311843917295",
  "points": [
    [
      "3602435210060898533551",
      "-212495763482503931933852626163250"
    ],
    [
      "236340280576014092161",
      "-5216968692394914838506738393870"
    ],
    [
      "28243280036724276571",
      "-10657857498611322415670962909110"
    ],
    [
      "445657333572671031313",
      "1546700562490240851642221329602"
    ],
    [
      "-212806122830110288634189/961",
      "444031907639804323097671812542779350/29791"
    ],
    [
      "-113778460646701765049",
      "-13417766692864652767300962259950"
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      "414789292870653250051",
      "107914596971221888853648438250"
    ],
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      "155569004273862943951",
      "7511384276628692038589439808050"
    ],
    [
      "-797234426270712020999",
      "-1326821882054410182072505541850"
    ],
    [
      "-641147386434665461199",
      "13047671970592584987814732193250"
    ],
    [
      "373362014832557086726",
      "-715473812797965370379554989525"
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    [
      "280019446222457639446",
      "-3882834193240866796064943354765"
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    [
      "299083094429856586351",
      "-3279196853472524006332928012850"
    ],
    [
      "383966458197008139331",
      "27037600750490460551388954090"
    ],
    [
      "162055822402389386401",
      "7335430669276849674734318572050"
    ],
    [
      "379174182642168416851",
      "-447303148135371616072767023850"
    ],
    [
      "157480791184194153793",
      "7459680257075430282017566069938"
    ],
    [
      "311670351930008079601",
      "2872884599404100172312502413150"
    ],
    [
      "39544698882072167671303/121",
      "-3160836386140562218499709696591222/1331"
    ],
    [
      "515515173176257230751",
      "-4178740978636424070494202838350"
    ],
    [
      "521518064109563087161",
      "4408174328044536745274773391130"
    ],
    [
      "484001516155337153251",
      "2986220813362387972095229756650"
    ],
    [
      "199420175507082952651",
      "6293524719668003299836953685450"
    ],
    [
      "520895340331597131451",
      "-4384336419617026378434733183050"
    ],
    [
      "414661859412507277891",
      "-82788920875138071265158180330"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 434/205 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -5184596861019629847612T^8 - 133754925365232341831388T^7 - 1035437637468603823145739T^6 - 1575565271267685915981924T^5 - 1170680387853697770352680T^4 + 900828146471472012207744T^3 + 1832423192062073064608256T^2 - 1187684595807033661235712T - 1681976130623118064380672,\nA6 = 149744321704475419746038421127284T^12 + 5524322875536651418776153811707324T^11 + 73960445444599888122367809067169241T^10 + 447433713175257084856032889546498740T^9 + 1270478308377182851928891301866983125T^8 + 510043107515189769341895147322518288T^7 - 1365617314830659026227384880724910192T^6 + 394471188044464447389716164705234752T^5 + 2190221113813265570364601521374517120T^4 - 625950896394979706215937393243105280T^3 - 1449978984373691606292352028569522176T^2 + 834866943439151412261391613342736384T + 852857001347003013712347074940788736.\nIt is a 2-neighbour of the fibration given in curve#4191 (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 02:33:31",
  "updated_at": "2026-10-27 02:33:31"
}