{
  "id": 4277,
  "curve_key": "1000591491754515346368656875587184890721:-27184084501265278732891378837415912485527358557919216806545",
  "ainvs": [
    "1",
    "1",
    "1",
    "-20845656078219069716013684908066351890",
    "31463060765353331858086739177380841883984296285897372831"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 269.40422983098,
  "faltings_height": 20.441511143820552,
  "conductor": "139883182700156075678240143523566742427129552398645127416507706029578508671711831046708338596405138",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "29",
    "41",
    "2417",
    "118643471271063007",
    "13154440207536530510113316253120360112142374009561177739898271696127"
  ],
  "discriminant": "152083955373867280930311974970586224458386900726854737681312823930051742678695328601122965967784699064123047411712",
  "regulator": "675552251745816771672819641.4338960459713444037902137550538777541836534417901974597844364",
  "points": [
    [
      "-2963791074259093519",
      "8198238768336341577216049491"
    ],
    [
      "1469350597212947669",
      "-2001449109157791658982545581"
    ],
    [
      "-4244925192654891175",
      "6592446384431972403826510707"
    ],
    [
      "3464623825039022575",
      "-910343805161394513098631033"
    ],
    [
      "4379865367338308249",
      "4917501126084878417666861811"
    ],
    [
      "25782887969646502889/25",
      "415736007743752361407461509127/125"
    ],
    [
      "108754883494123334641/25",
      "-600837297398942189550744496729/125"
    ],
    [
      "-92360059976517777511/25",
      "952397045510555029754082092103/125"
    ],
    [
      "-4933096136084511175",
      "-3774603761866059386331253293"
    ],
    [
      "6699315156700765399",
      "13873796255383843242489260289"
    ],
    [
      "-1888478018493618689",
      "-8005913559040357870981568583"
    ],
    [
      "1262586989250574361",
      "2675131630899847277278910067"
    ],
    [
      "6300948488000652001/9",
      "112016032032709163852235082273/27"
    ],
    [
      "1740030122671711097",
      "-677708540978997416707735821"
    ],
    [
      "33961756486786070129/25",
      "-297169834305664678578962514393/125"
    ],
    [
      "15184105502609755249/9",
      "-28267297132113862139791884191/27"
    ],
    [
      "40225633551772314201",
      "-253539139274396117421618481613"
    ],
    [
      "16050285443116016153",
      "61900121574771199559138998899"
    ],
    [
      "3571481766423556121",
      "-1602857321075756450593053069"
    ],
    [
      "109043022844621460129/25",
      "-606219884544809375101292784393/125"
    ],
    [
      "7924928136995196113",
      "19078358741535993866217080667"
    ],
    [
      "9401268147942768481/9",
      "88845189504244750043317772833/27"
    ],
    [
      "201125852238465521233/121",
      "-1578205936563334418497148618391/1331"
    ],
    [
      "6310199776447645711",
      "12295782247407015168247600617"
    ],
    [
      "-53172261685998452111/25",
      "1016874440240253144435268249127/125"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1790/379 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -48393752778478434415347T^8 + 234108952651394609784372T^7 - 80814256417092311126712T^6 - 679388493916744317276048T^5 + 849130008583102656447600T^4 - 1612877972465689819445088T^3 - 1721372370991450068420576T^2 + 3195581161738120242427584T - 1022262851511189811019952,\nA6 = 4288640503583697356313758651467086T^12 - 31081375829532514009215543683973804T^11 + 28276823001661393553469125282330460T^10 + 256926134808356645699750469379877640T^9 - 449617863421297320058465556298389964T^8 - 1048634128416718070202997112516438256T^7 + 2065736410495836489928705601739523680T^6 + 2236546605261081463863864681224077632T^5 - 3826369071427309561101765341099280384T^4 - 533037124876780800676744763435971200T^3 + 3060828262346510699070310919653538688T^2 - 1792851678299100321486790706293201152T + 349240517064527681543842990887408000.\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 08:23:05",
  "updated_at": "2026-10-16 08:23:05"
}