{
  "id": 4275,
  "curve_key": "57470630647667255384639258425443179836518958801:-13734612999100952809518335900910548299250270622361100791804040551953049",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1197304805159734487179984550530066246594144975",
    "15896542823033510196201677887690482405517585258649841003511904830457"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 323.00280969210695,
  "faltings_height": 24.733533239982602,
  "conductor": "366606529437414781286685203550676921309473368465239452431786719081938621846001976326937135318223990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "89",
    "103",
    "149",
    "111697",
    "1615515320713926448564207",
    "10367116736264996759085139193022296339940641734673489"
  ],
  "discriminant": "682073071496910640466714209685740303862015058694647589172412713657280723783631477304716361147370697213239454105692985762839763353600000",
  "regulator": "719225472036500953171648023.971609363868281735443665608596403207238178342290054082600671429",
  "points": [
    [
      "30661225339747830803054",
      "-2830310515617653731816292612560627"
    ],
    [
      "9397766098888623551174",
      "2339774410761436690381560416628893"
    ],
    [
      "16505010438998747040454",
      "794501752072535124944732273980573"
    ],
    [
      "76688914640409893203604",
      "-19367462049642845027522787961208227"
    ],
    [
      "18876785638346053744454",
      "147305836213727590093487104642973"
    ],
    [
      "530675711255784904436054/25",
      "26791189732690690205293093876466857/125"
    ],
    [
      "-22214522400445898184506",
      "-5615297278753237778003900927621987"
    ],
    [
      "-37779798369101820156046",
      "-2684562044754718392974270089416427"
    ],
    [
      "18404149863770689994054",
      "-308035128828395619195589499542627"
    ],
    [
      "-896961626855358165946",
      "-4119436569150785998345320379222627"
    ],
    [
      "15023504861152953101878/9",
      "-100672566914940829762929057965815729/27"
    ],
    [
      "18185014136443311051974",
      "370440982778492149096978110578333"
    ],
    [
      "17513870350102229078054",
      "547019362567679133669779662532573"
    ],
    [
      "20211336497515302890699078/961",
      "-4016002126690286094078289382762732989/29791"
    ],
    [
      "24272554428556624365254",
      "1065476258621863328908392479266973"
    ],
    [
      "55992900861215316920924",
      "-11153707604938988824854431117738857"
    ],
    [
      "11259810788037638001254",
      "-1960273876111769500542514772005027"
    ],
    [
      "13984759886553828108998",
      "1373889069960413798848281953342621"
    ],
    [
      "29031921188858918767334",
      "-2367722518032937764527020630667587"
    ],
    [
      "37793198574902366731214",
      "-4962616987832565571661947332344347"
    ],
    [
      "19038853154123618001782",
      "48954333715298638145367428587325"
    ],
    [
      "21303608062133570330054",
      "241120675241006140158380656585373"
    ],
    [
      "18947016161791544481734",
      "-113875804841252069971310760652387"
    ],
    [
      "3185837787751513089687494",
      "-5686040883792595499460639393368389987"
    ],
    [
      "103861784268668758202054",
      "31810807331334944654090280821641373"
    ],
    [
      "26865820478120535420852422",
      "-139251474515920052188232752113876680035"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -14911/6170 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25598589065575488253872T^8 - 219912513106757586234048T^7 - 324549648424331055742464T^6 + 1523547434916270832355136T^5 - 2849165156820063127691880T^4 + 3746564993881929295112904T^3 - 973581348748449447744444T^2 - 862126587120769476566112T - 118556909623229874930432,\nA6 = 1625048868702522016795790220948864T^12 + 18521876511799709835187838396715264T^11 + 69457772033476867393403462775818496T^10 + 74100738882710387630246485913752320T^9 - 324420440712638126863027033199077920T^8 - 1791949805594601002560679464033967520T^7 + 4689003940396889037978292829416265040T^6 - 2864400878761409044683373393741992480T^5 - 91393345783003551423720760724759820T^4 - 338626380479684457921000808774737600T^3 + 374448354510478802333765563563322320T^2 + 177989462843015858245005305484080640T + 17806843321561611911434592141844480.\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 04:40:41",
  "updated_at": "2026-10-16 04:40:41"
}