{
  "id": 5629,
  "curve_key": "1094948701445602782651457425:-31729293652718835129045996216864098660025",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-22811431280116724638572030",
    "36723719505467317590512154432159757197"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 186.78151507504623,
  "faltings_height": 13.549881161591909,
  "conductor": "136034978365298402045363153712823092844398059119150",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "67",
    "1478957",
    "40937000295131",
    "71531877443741033941"
  ],
  "discriminant": "177083207868320200046851204413560033169952464786048310778877094151746170880000",
  "regulator": "128854529015734.358761673585193980160068463946187527825230588400091200396",
  "points": [
    [
      "-5281094948551",
      "-3146981117744339165"
    ],
    [
      "-138817227971",
      "-6315668075998896905"
    ],
    [
      "4148002799519",
      "3670430188193063005"
    ],
    [
      "1853329404505",
      "-901385624907515037"
    ],
    [
      "1917124949409",
      "193636060208679435"
    ],
    [
      "7020708425309",
      "-14920608884842636265"
    ],
    [
      "-266674046151",
      "-6541251401815478365"
    ],
    [
      "10386626781109",
      "-30336783728608232165"
    ],
    [
      "520323044729",
      "4999527351912104995"
    ],
    [
      "998374523769",
      "3865811079022662755"
    ],
    [
      "1795637009129",
      "1245937987555961795"
    ],
    [
      "-463695241431",
      "6870340180273214355"
    ],
    [
      "19419465711609",
      "-83169248721269971165"
    ],
    [
      "15998630543705",
      "61373605271080908131"
    ],
    [
      "33011844701041/9",
      "-41838554220924333695/27"
    ],
    [
      "5644016643129",
      "9368313044944647075"
    ],
    [
      "104913182949781/9",
      "-993819397586479797155/27"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -8/9 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 583074314969616668304144T^3 + 1749298418924942437857936T^2 + 6981774061823935535232T - 733152591313571732712192,\nA6 = 99353320243156880097765275026566T^12 - 1192047168420920079142624551372696T^11 + 51816962014333011197785218484470384T^10 - 160733095313938224161654547702105120T^9 + 1161258380951665950605765814917343480T^8 - 500375410396179478662655437513305328T^7 - 2173656091315178125605895871772822192T^6 + 963181788398399075637606795285979968T^5 + 1772421005485324185894755005716179280T^4 - 460279153080260982936199267860712320T^3 - 927109903404780261014801473928185344T^2 + 58145438007481575316035550439430144T + 241998303936746269490887631501697024.\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 00:00:01",
  "updated_at": "2026-10-24 00:00:01"
}