{
  "id": 4218,
  "curve_key": "3166511171008151541029490275512165441:-4562753155339494262731125347696029424216702912576699489",
  "ainvs": [
    "1",
    "0",
    "0",
    "-65968982729336490438114380739836780",
    "5280964300161451687478424295351622815593133679755152"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 252.1370812578787,
  "faltings_height": 19.017562077236597,
  "conductor": "90265477399337853384281373437352459166657125981023179406109763937548861121056230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "53",
    "109",
    "167",
    "14037829051847",
    "4658169625016392513277",
    "21358837834525765320169690094860937"
  ],
  "discriminant": "6325946571202494455758740084079538261526315235374602315702496053752203480506518093665022392975250944000000",
  "regulator": "26785346404809403135601.7172496427841537805677004776612063338134973280234995788247555",
  "points": [
    [
      "-227692964516182856",
      "92179736983824910309241428"
    ],
    [
      "210735424378337014",
      "-27158801750052234432693062"
    ],
    [
      "51396726076626394",
      "45012724421917861284508678"
    ],
    [
      "446574852116491744",
      "-254717286215107117300988972"
    ],
    [
      "-185639902584213656",
      "105498271685086370839356628"
    ],
    [
      "81797942134056304",
      "20787962635589763257571388"
    ],
    [
      "33179861933806744",
      "-55934339904765336808148972"
    ],
    [
      "71893505586930904",
      "30163174848254404716673108"
    ],
    [
      "275161996300016344",
      "-89232600030245633170652972"
    ],
    [
      "1077810822099415252",
      "-1089149222036972088947005052"
    ],
    [
      "81164740474867744",
      "21477875172335060595222028"
    ],
    [
      "-76274483635438856",
      "-99342664224873497185482572"
    ],
    [
      "182487974337689025496/2209",
      "-2063389481272616072667601454356/103823"
    ],
    [
      "-83914743504716276",
      "101122863151977211348759108"
    ],
    [
      "91573077322307044",
      "2807017936036955966461828"
    ],
    [
      "79893193567205944",
      "-22813234063956296936608172"
    ],
    [
      "-277970085393556232",
      "46263928612344660614534836"
    ],
    [
      "88193621474212564",
      "-12202496788935187779532412"
    ],
    [
      "922334624194741144",
      "-853853981645091004475622572"
    ],
    [
      "-63367348694353856",
      "95952057105467179804616428"
    ],
    [
      "42492739694793544",
      "50541940771079651629980628"
    ],
    [
      "-290117537441740556",
      "-1027813001702662062850172"
    ],
    [
      "2361689947621851736/49",
      "16136945297702013978849463564/343"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -973/82 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10490924381115083744475T^8 - 198606534222460688122680T^7 - 1065417976804438457255016T^6 + 1639325103621379811930736T^5 - 2065857830370934339051440T^4 + 1624515338975555277541440T^3 + 627292956712495652706816T^2 - 579571543143419272734816T - 175069545700351062329712,\nA6 = 377475523351270352670804404613750T^12 + 8093831427752091624508772362041000T^11 + 59608190005431403688311326659353800T^10 + 258877237945365511005499173975059280T^9 + 1166329210851912140109373033476192096T^8 - 3290737074386209591354797503931856128T^7 + 1076110014915408676877000781319873728T^6 + 1655411108858774108267005356846449184T^5 - 323687792595432052178005121163318384T^4 - 745457216313233319000016951349121600T^3 + 632802115601259765911745996693312T^2 + 143229663791151165669809219876399232T + 28115415195462890182082065162444416.\nIt is a 2-neighbour of another fibration built here (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": "2026-10-14 05:25:04",
  "updated_at": "2026-10-14 05:25:04"
}