{
  "id": 4586,
  "curve_key": "1498932977325432938070356295599281:-49540570629004475696300773720286075878432212862825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-31227770360946519543132422824985",
    "57338623413199622046182069134417440709372418361"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 229.1701847260008,
  "faltings_height": 17.090497916799773,
  "conductor": "8917119221745677058307104421347510559180898815516214720856080386319147814",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "43",
    "60373",
    "990488237",
    "567570027575987",
    "191026498937557279",
    "13951228500613746619"
  ],
  "discriminant": "528665845429798837652124830665293323627820929530888796631863325982429548450550339772692063875072",
  "regulator": "4975707355249486941328.852716873558057302087017412908310792619952281746303139149034",
  "points": [
    [
      "-446211786590630",
      "-266803259948038835813741"
    ],
    [
      "2143098202723570",
      "-16044193777650374553341"
    ],
    [
      "2048202270794746",
      "-44388211700396909844077"
    ],
    [
      "-526112283562748",
      "271334318391031004610169"
    ],
    [
      "-25346990506293101/4",
      "222424668176839868244059/8"
    ],
    [
      "243619119614716330/121",
      "-68217739882670283951782551/1331"
    ],
    [
      "-121216541355350",
      "-247228972030883135443469"
    ],
    [
      "5169617404315066",
      "184555502459545433897011"
    ],
    [
      "4297913792947594",
      "50156679218166101536195"
    ],
    [
      "-17893620397940366/25",
      "-35205439163666073740350033/125"
    ],
    [
      "-6099077307047750",
      "144641607045284938368019"
    ],
    [
      "-5648363395865306",
      "231341701497791845768411"
    ],
    [
      "4590107234933338",
      "-103485100815692554433261"
    ],
    [
      "1497459801189978",
      "-118043108532610167936237"
    ],
    [
      "38334144739253338",
      "-7429167501576822118980077"
    ],
    [
      "5312873247781438",
      "-203454919909994164583477"
    ],
    [
      "1572352950048076",
      "-110112965562400781575199"
    ],
    [
      "11883601065754666",
      "1168093353019403701789411"
    ],
    [
      "673630125188869876/625",
      "2467223335301803220657378299/15625"
    ],
    [
      "-5479883124610724",
      "252798524200952673092851"
    ],
    [
      "4596136748446036",
      "-104414978139416421239159"
    ],
    [
      "814468811654746",
      "-180124579450990228644077"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 31/117 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -80980973155382618456892T^8 + 285465051520066035306000T^7 + 261576072020933408151900T^6 - 951872800330750729557600T^5 - 740266115548451074781940T^4 - 838297434410400458533680T^3 - 2411861402496464207592220T^2 + 321039963467228344391680T - 16364003227722838984000,\nA6 = 8727598530781278063259830058307124T^12 - 48350067107354860665788856770508000T^11 + 6795007788217678621771300867414800T^10 + 321740442330556067264524621932532800T^9 - 148612015016082982201355258151421080T^8 - 1249986278690606236857933073188907584T^7 + 185359528793598231769817920929440640T^6 + 3119211110386308385542728766215321280T^5 + 1959126383802129619521972397334285700T^4 - 734642679786885593606821730974577760T^3 + 302738566919351785316592492519057616T^2 - 31992857837231850069180957876807040T + 1040209640416816878466851126534400.\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": "2026-10-18 12:01:17",
  "updated_at": "2026-10-18 12:01:17"
}