{
  "id": 5676,
  "curve_key": "656749969210730794495473656072762241:-543842161125790500237524846870431374977905168024372545",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-13682291025223558218655701168182547",
    "629446945747442712028819106850370312740204421703475"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 247.46099760492544,
  "faltings_height": 18.52055344139012,
  "conductor": "51067301631369846866482631889409436113279841426348090994970974832467991732615078884934278443806",
  "bad_primes": [
    "2",
    "29",
    "149",
    "7229",
    "97671961349",
    "8369133874567228077277470697712414255723669352613065342160208844200735450783"
  ],
  "discriminant": "-7230646201520917981104421352051119667461560559312899315769985671203854492520603840079495730157509869568",
  "regulator": "246987248692668316421901793.56250519033321547208987073467939584744427329451042855800138",
  "points": [
    [
      "102971965631609771",
      "-17674544954332180507165934"
    ],
    [
      "130489849102225387",
      "-32649286471722596913279678"
    ],
    [
      "165071669342415163",
      "-53561828489151869999127678"
    ],
    [
      "5835547273726419291",
      "14094050102144854885026683202"
    ],
    [
      "131759146953982371",
      "-33377852596107527756585638"
    ],
    [
      "-33276343968731241",
      "-32371224413417365164509290"
    ],
    [
      "139528371732378423",
      "37904362902604905292226514"
    ],
    [
      "64902411122250559",
      "3850089015752807617228270"
    ],
    [
      "100674893471942987",
      "-16503560582842479877644478"
    ],
    [
      "-1043856610148474669/9",
      "-691601600920467027722709130/27"
    ],
    [
      "5595493435304893795/121",
      "13015115100008779503264485414/1331"
    ],
    [
      "-36657590090590497",
      "-32889923440829322502256686"
    ],
    [
      "947948636398512395",
      "-916238100154513759820092606"
    ],
    [
      "91097801716532987",
      "11790827371389631002035522"
    ],
    [
      "101001490061949125",
      "16669186065720058699903774"
    ],
    [
      "96085844061960859",
      "14208589026020623458185250"
    ],
    [
      "114301737850666491",
      "23640571514183449690691906"
    ],
    [
      "56957988956292187",
      "-5908890340667040026226078"
    ],
    [
      "849016639550624110691/11449",
      "5825884703512736457189579893350/1225043"
    ],
    [
      "-3936540709755733",
      "26138990788673674327234882"
    ],
    [
      "259407495657394451635/2601",
      "2126121080410986429006474362134/132651"
    ],
    [
      "53605988105562683",
      "-7073647482099282639215998"
    ],
    [
      "-104996117203466773",
      "-30141960676528473771946798"
    ],
    [
      "347817530583299892651/5041",
      "-1333260491005760089931728237938/357911"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 129/376 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25474223654459729695152T^8 + 93424157542535492313792T^7 + 249549530991798533589216T^6 - 697407234931421362933344T^5 - 624235669206688152877680T^4 - 597548430366277034810016T^3 - 3503195429735821784150304T^2 + 3443481263994739372563948T - 932157668798019061834527,\nA6 = 1558176592694379366370572668882304T^12 - 8556444096428535116807109681029376T^11 - 10909694949700311770505743225764224T^10 + 132365209573836556400929013899470720T^9 - 65939622169833360804191934552439680T^8 - 921173694379955547822888188003154432T^7 + 724370040233725908757397970764697408T^6 + 3685802165670854989077288042679139952T^5 - 921815011359411216952545051496976700T^4 - 3541405794655636698734958615621659160T^3 + 4046594122834363561792364624080217124T^2 - 1844492709789748579332256815007671156T + 328955182757185562525000064586958946.\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": "2026-10-24 06:15:27",
  "updated_at": "2026-10-24 06:15:27"
}