{
  "id": 6007,
  "curve_key": "2352155606611104790980547528746460816:-3602064654674892257405431126969723668050561026297699864",
  "ainvs": [
    "0",
    "1",
    "1",
    "-49003241804398016478761406848884600",
    "4169056313281125281588538758452656159915828534512656"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 251.24518660472108,
  "faltings_height": 18.725302728848032,
  "conductor": "1652702000228020271965360611404321303811592321821438740333392388568027778059779929380885",
  "bad_primes": [
    "3",
    "5",
    "13",
    "19",
    "23",
    "29",
    "103",
    "32797",
    "39778113426263",
    "6892286526747529",
    "1915403630441793766415352356899227989701619"
  ],
  "discriminant": "22425350057107283047258180304100485879309103583510003340500726335550819636762625722983813442066104703125",
  "regulator": "4133235204131110976155240.9999634305148840516836220861120517709462011127448261580432633",
  "points": [
    [
      "98218300488716000",
      "-17422309821030071079995888"
    ],
    [
      "123180501781478405",
      "1372538335598727018196117"
    ],
    [
      "23213118431479175",
      "55172879391262953395407312"
    ],
    [
      "138364261300018550",
      "-6139781491270662906320813"
    ],
    [
      "115939526858147450",
      "6789678680812637818703587"
    ],
    [
      "23283769808497207325/196",
      "-13493922257504603846912360647/2744"
    ],
    [
      "212657741943677450",
      "-58010565061050764255250788"
    ],
    [
      "77322724722129800",
      "-29022224827367874851416688"
    ],
    [
      "132177633064057874",
      "1090658254284491732509027"
    ],
    [
      "123725908678302155",
      "-307139483490693353080133"
    ],
    [
      "554749342756735160",
      "-384326545572769002165444848"
    ],
    [
      "-254355658776680050",
      "13315805906605814863920787"
    ],
    [
      "-68050175609157062",
      "84785653112558675069138716"
    ],
    [
      "368732203277632445",
      "-190352517597875449779589283"
    ],
    [
      "123710339197415738",
      "377309075563326695665891"
    ],
    [
      "38914847927082200",
      "48177109806994695021602287"
    ],
    [
      "103312868620106513",
      "14460490240474793528133958"
    ],
    [
      "147426296313726200",
      "12203630508261713825858287"
    ],
    [
      "122016263074287950",
      "2537350070962839545981587"
    ],
    [
      "261693042571388705",
      "96264419920788249854485417"
    ],
    [
      "-113262496489618225",
      "-90919249812252104782282088"
    ],
    [
      "6550354887336751075/49",
      "-921234517613216302246165484/343"
    ],
    [
      "8812465984853606825/64",
      "2907079559246467567787442869/512"
    ],
    [
      "806080548403156355",
      "-698879180833120940275685693"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -65/21 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -42783457648311062145792T^8 + 356652061732127265219072T^7 - 776392718276863895491584T^6 - 594563894687761097733504T^5 + 1610134904768785320105720T^4 - 1299142963618345803173436T^3 - 1310847137770922715048759T^2 + 2293995846725083806581718T - 762637489081909275352167,\nA6 = 3393863243684538700888419573325824T^12 - 42546028233387428372499985647230976T^11 + 184326642514085964348103427989426176T^10 - 202262449736636480735819511193036800T^9 - 605066230051264992235683353165205120T^8 + 1246062737155179656440992962298863808T^7 + 1477591518827520114475641040966728528T^6 - 1553487810870706704105291467455269168T^5 - 2067093448474470395926495237989292755T^4 + 1400402544246467407554684971457155760T^3 + 1384929818086858833031645353525974259T^2 - 1332090731990002399128362594486258406T + 294374686993228956276286908014904426.\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 22:26:22",
  "updated_at": "2026-10-27 22:26:22"
}