{
  "id": 5947,
  "curve_key": "1139204074625373686258161:-1085774924115597325976180129313760841",
  "ainvs": [
    "1",
    "1",
    "1",
    "-23733418221361951797045",
    "1256683939938719091917233595679195"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 166.17711621080716,
  "faltings_height": 11.825332339332812,
  "conductor": "2065481983464558195030515876385280289303401125856240470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "53",
    "61",
    "15053359747",
    "108822239426510950433358741959562548723"
  ],
  "discriminant": "173342492110758130625462503371534380333372067370284303248976384000000",
  "regulator": "3900184099006324.1014543912276433548202148843837110886414430652144959114066",
  "points": [
    [
      "-172460339477",
      "-14843896043844412"
    ],
    [
      "323822263093",
      "165914138594611268"
    ],
    [
      "463027526823",
      "299228792384612588"
    ],
    [
      "-146271433577",
      "39983558755864988"
    ],
    [
      "63556350823",
      "2237070622604588"
    ],
    [
      "-130150128257",
      "46270693657579868"
    ],
    [
      "210120057703",
      "-74476339191435412"
    ],
    [
      "122236046823",
      "13491161498900588"
    ],
    [
      "384001486743",
      "-220832204507310132"
    ],
    [
      "42881710414943/841",
      "326399101768705493532/24389"
    ],
    [
      "63972506823",
      "-451684278227412"
    ],
    [
      "127159181023",
      "17171333167715588"
    ],
    [
      "106528963622383/121",
      "1083579099658968234628/1331"
    ],
    [
      "-803351756093/9",
      "1393568268475963376/27"
    ],
    [
      "544530025823",
      "-387031703665100412"
    ],
    [
      "368883544423",
      "-206634330684171412"
    ],
    [
      "45205103473",
      "-16618957731101662"
    ],
    [
      "123239296743",
      "14266797672029868"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 3/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25598589065575488253872T^8 - 219912513106757586234048T^7 - 324549648424331055742464T^6 + 1523547434916270832355136T^5 - 2849165156820063127691880T^4 + 3746564993881929295112904T^3 - 973581348748449447744444T^2 - 862126587120769476566112T - 118556909623229874930432,\nA6 = 1625048868702522016795790220948864T^12 + 18521876511799709835187838396715264T^11 + 69457772033476867393403462775818496T^10 + 74100738882710387630246485913752320T^9 - 324420440712638126863027033199077920T^8 - 1791949805594601002560679464033967520T^7 + 4689003940396889037978292829416265040T^6 - 2864400878761409044683373393741992480T^5 - 91393345783003551423720760724759820T^4 - 338626380479684457921000808774737600T^3 + 374448354510478802333765563563322320T^2 + 177989462843015858245005305484080640T + 17806843321561611911434592141844480.\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": "2026-10-26 05:20:26",
  "updated_at": "2026-10-26 05:20:26"
}