{
  "id": 5823,
  "curve_key": "28730637520404074788624:-4802686158756316416773291872763032",
  "ainvs": [
    "0",
    "1",
    "1",
    "-598554948341751558096",
    "5558664535398070129225541000036"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 155.13675304703781,
  "faltings_height": 10.807405986161745,
  "conductor": "576566883287261159483617520220511010982249603410435415",
  "bad_primes": [
    "3",
    "5",
    "11",
    "17",
    "29",
    "62099",
    "114139042169872969595679340119291317845632493"
  ],
  "discriminant": "376097780797317115066904639935164157402387422701173966173230325",
  "regulator": "19495258720948234.563623353203309045319515959614392270031194401428298874970",
  "points": [
    [
      "12017954994",
      "-317846305432112"
    ],
    [
      "62505141813/4",
      "1162422038641211/8"
    ],
    [
      "19972285389",
      "-1253372577492239"
    ],
    [
      "-18073016103",
      "-3236216590600043"
    ],
    [
      "16706234832",
      "470899621469227"
    ],
    [
      "-1311011724",
      "-2518158808822757"
    ],
    [
      "11959602557",
      "332854673795902"
    ],
    [
      "63951651141/4",
      "2201733928026563/8"
    ],
    [
      "12677590212",
      "89380532053147"
    ],
    [
      "11736103182",
      "387875228966527"
    ],
    [
      "35104241253/4",
      "-7926202243616749/8"
    ],
    [
      "8796994449",
      "986891061027613"
    ],
    [
      "-19493739168",
      "3133528893712852"
    ],
    [
      "-22213825953",
      "-2809511932691333"
    ],
    [
      "17087477387",
      "565777537473952"
    ],
    [
      "-5349060804",
      "-2933823717590684"
    ],
    [
      "59142414057",
      "-13305205849817723"
    ],
    [
      "37636635411",
      "-6028596739927064"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -13/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -131683424850520935576768T^8 - 403203691800547711440768T^7 + 228773565844968202575408T^6 + 1001632750223305381512624T^5 - 240565012803414935795880T^4 + 1113998583596965801461504T^3 - 955469793798674292115872T^2 - 990503756503270017161688T - 226533255431841379251243,\nA6 = 19076424418751512058704915856577792T^12 + 97086137010965231517170399109938688T^11 + 56104518594343130212702088417622912T^10 - 478767125533383624912178730778518400T^9 - 714366843201118889959457857278267504T^8 + 1042906926398973532541608382597231424T^7 + 1920199847343299876864028118527850608T^6 - 1651848617855242258127597768465390256T^5 - 1294346250171073842969926939033547144T^4 + 242314299085392499926732997139536320T^3 + 623077991032626826626842144461126512T^2 + 269831263748284750614515352678364488T + 41099644923330823113323890449407142.\nIt is a 2-neighbour of the fibration given in curve#4647: 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": "2026-10-25 11:01:33",
  "updated_at": "2026-10-25 11:01:33"
}