{
  "id": 4607,
  "curve_key": "2369768204068252194379143173651445279361:-113256586992362636046989797321961493835987826688570414364609",
  "ainvs": [
    "1",
    "0",
    "0",
    "-49370170918088587382898816117738443320",
    "131084012722641939865086973397985087435670268435293109312"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 271.9908323188232,
  "faltings_height": 20.55781998136829,
  "conductor": "38938275751421165657965390788800553681436254990327719933556824785334970630362562521910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "29",
    "41",
    "71",
    "1051",
    "21405158469588865084313073193",
    "385900670961641322828141340373091638822278871"
  ],
  "discriminant": "278410278436078887242027930949421365246835245842724473608561432853047376426476257767241141416653559867418624000000",
  "regulator": "706079748940218750438424.97259291173698926205429528727837066422782961769642587458733802",
  "points": [
    [
      "6520550819144364464",
      "-9295233451784892691047723832"
    ],
    [
      "996154257209098064",
      "9104516124338530397011092968"
    ],
    [
      "6220003627532189264",
      "8040126833622198126988282568"
    ],
    [
      "586206676512376304",
      "10116537547537493381517585608"
    ],
    [
      "-3617390020297312336",
      "16196906527305460220697893768"
    ],
    [
      "-1480752900039860986",
      "-14175411616247854506053217082"
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    [
      "281192301017510808464",
      "4713796091648297372967733268168"
    ],
    [
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      "-1878400035844248314682576952"
    ],
    [
      "4694168104486978964",
      "-1664070531819228493668878632"
    ],
    [
      "1069989532739878064",
      "-8915349329594500128629447032"
    ],
    [
      "3354706217707065254264",
      "-194303573797498707914736017331832"
    ],
    [
      "4930772184078574064",
      "-2744160461736608124862607032"
    ],
    [
      "-731521848874093816",
      "-12915413906143775265186074512"
    ],
    [
      "5117490435914674664",
      "3528894980250670819946309768"
    ],
    [
      "4810672666846125464",
      "2216216846490160354854150368"
    ],
    [
      "17817212686720462664",
      "70054079146741990435484818568"
    ],
    [
      "3216867450842062864",
      "-2357036498397366645819730232"
    ],
    [
      "103466385306023966996/289",
      "-52330860709853456898780526860716/4913"
    ],
    [
      "68979723666771081382526/9409",
      "11658418300355553491173878852162164/912673"
    ],
    [
      "923375241833105864",
      "9288924001108939869090216368"
    ],
    [
      "6642842996605639724054/961",
      "326484787968219388420588812416588/29791"
    ],
    [
      "3386328218200920944",
      "-1652929648328577837336935992"
    ],
    [
      "-3619889933139968656",
      "16197684909701806675554283208"
    ],
    [
      "33364135133016849392",
      "-188742405335756459751036991672"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 135/188 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 another fibration built here: 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": "2026-10-19 01:29:06",
  "updated_at": "2026-10-19 01:29:06"
}