{
  "id": 4217,
  "curve_key": "206447881050986848958233909363992945538753921:-2950416928697338164595847579485910028666386833244920749724655431745",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4300997521895559353296539778416519698724040",
    "3414834408214511764576735208770865309374074165422095836380919881"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 306.11586568286964,
  "faltings_height": 23.3483410756164,
  "conductor": "181067958205627543116788725873078333477524043431875412351138736291524758324425666817398010082",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "43",
    "53",
    "61",
    "71",
    "157",
    "86399",
    "10262801279",
    "1047973045800633191898460783061214030886355968884601207808011"
  ],
  "discriminant": "54397480760610627491991106755775836752382704750033260516000923468729308610097682849464633956735419009640455785470770124460326912",
  "regulator": "222159866642113008061909747.4329240233444382915770442679225668901379276595025353719749910",
  "points": [
    [
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      "-40295573889456964644901846477923"
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    [
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      "-7836969901302937881747116634371"
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    [
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      "-51035307082167995866787277328179"
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    [
      "-988682944646254991131",
      "81857960464668594728700383877261"
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    [
      "1276139463301652048101",
      "2096569058617912808400219396237"
    ],
    [
      "410320290322361575661/25",
      "7228683498125580146029946542295001/125"
    ],
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      "1122740432909793891377",
      "1093910302874945358642456434589"
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      "-35954506615232459249207095379571"
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      "-825696971775346138011",
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    [
      "-21533235148842876729707/9",
      "81515834221886335450369854871303/27"
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    [
      "-886727747455490054203",
      "-80817241674747377295548815341171"
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      "605223477800830992287",
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      "-882815553721409594011",
      "80769968875951263382469770610061"
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    [
      "245574901714771577509",
      "48717833059673084057584545772429"
    ],
    [
      "1292219801940407585429",
      "-3845808107481182523074654042739"
    ],
    [
      "982383258775803238629",
      "11733789002277734341573193605261"
    ],
    [
      "1316196435321650153819",
      "-5832670314328121450533846531989"
    ],
    [
      "422419361292044215108781/841",
      "-906417850834564774977419668203930111/24389"
    ],
    [
      "63101036091645440851237",
      "15842474067371249214906651732480909"
    ],
    [
      "28019392869275425216649/25",
      "-186665999457663096240333686101203/125"
    ],
    [
      "589420538844167559557",
      "-32931938815583985126155549189907"
    ],
    [
      "31744128394505724381",
      "57256746143000593057544400694741"
    ],
    [
      "2204745406662658987269",
      "68185643018435627364099483301261"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -63/683 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 05:17:07",
  "updated_at": "2026-10-14 05:17:07"
}