{
  "id": 5691,
  "curve_key": "110500487976472888718752496161:-36729977156566735687366789604060392449777841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2302093499509851848307343670",
    "42511547634915011500734751035564021204900"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 200.6244523435919,
  "faltings_height": 14.398109503831101,
  "conductor": "25030165697049159938174890100368185460586439580530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "23",
    "31",
    "41",
    "1975522691",
    "239189952219046291165793612317"
  ],
  "discriminant": "92174827087547871784123104866950398773827784268717772768674230567801515008000000",
  "regulator": "24589599457194.4704343433750689922034659437873176904747158560527158011576",
  "points": [
    [
      "26273754404140",
      "12804216458685447130"
    ],
    [
      "26954328065740",
      "-6591565312370036870"
    ],
    [
      "27924828077740",
      "1285413975933015130"
    ],
    [
      "25077855715276",
      "-23482209255339889478"
    ],
    [
      "27445925135740",
      "1701609909731373130"
    ],
    [
      "30776325171340",
      "28501855208210091130"
    ],
    [
      "27874948318240",
      "-19681551584888870"
    ],
    [
      "182232327016840",
      "2382158588711130651130"
    ],
    [
      "23413280987020",
      "-38035764213978020870"
    ],
    [
      "1449161690006860/49",
      "5898442436933366326390/343"
    ],
    [
      "432401664331660",
      "-8938330052007191944070"
    ],
    [
      "26612990402890",
      "-9728289762167890370"
    ],
    [
      "34653079495660",
      "-65951371642505091590"
    ],
    [
      "13946672067340",
      "-114532827576459188870"
    ],
    [
      "14508815641420",
      "110295442825600971130"
    ],
    [
      "27907538336140",
      "-1016158371137723270"
    ],
    [
      "28022993000140",
      "2474166645744267130"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1/10 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -951794051889111932592T^8 + 44931125401781237315136T^7 - 935996917001646313472256T^6 + 350884544094515993044032T^5 - 1398456319949084806406280T^4 + 1757156899789831824711432T^3 + 1161615213018494249920164T^2 - 1209850628288081766896304T - 608061871140582830645232,\nA6 = 16573004223094294578838161979776T^12 - 853911819873454385971944861242112T^11 + 10730626760581365984133349196446976T^10 + 28681501792522102389650863794343680T^9 + 1144251410928840595115561345197638240T^8 - 1598280314283758871148427065729397664T^7 - 426571032276915684981278470103405232T^6 + 1752000471251825933878865739300711456T^5 + 357646791216195149324748670252742580T^4 - 1462595841433547195589341024424494400T^3 - 249356805352454598151173826415660496T^2 + 545782915696199470675908824491330752T + 182530075488483105810112141784098944.\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": "2026-10-24 12:28:30",
  "updated_at": "2026-10-24 12:28:30"
}