{
  "id": 4262,
  "curve_key": "355295494903272027856255434694200287841:-6691547387761968921632670089301033347722758565163495897361",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-7401989477151500580338654889462505997",
    "7744846513613389957443865528201108186430449098712265269"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 266.2980395131025,
  "faltings_height": 19.95790839380662,
  "conductor": "4223028627486731438810676051333745103263583487883191927128586549581983840471922130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "43",
    "47",
    "53",
    "101",
    "5881",
    "226814744989081168657109",
    "3248339536530584000120383370373029222214941"
  ],
  "discriminant": "42755099277003039928882741297185520815766552859283207267986325750279958166451293266988599175226011885568000000",
  "regulator": "132275760788821354494241.38410798703234125375961425133133275379613219392331456022932936",
  "points": [
    [
      "1312635203679634927",
      "538905999620598182032370936"
    ],
    [
      "1610695042098043279",
      "-34452150226681074977792392"
    ],
    [
      "5248002159767859727",
      "10650689232950484817831414136"
    ],
    [
      "2095626077077016719",
      "1198456416877553215427199608"
    ],
    [
      "1488707630702698927",
      "-157471246004457433758513064"
    ],
    [
      "2258499626867844727",
      "-1596138273075185181054238864"
    ],
    [
      "14614075526633389327",
      "-54961052685390411269500393864"
    ],
    [
      "-1002781097107188593",
      "-3762851993126835280433565064"
    ],
    [
      "1682495446074322127",
      "232003810122712235466127736"
    ],
    [
      "2723228993506127609143/1369",
      "-47838371940087130545726807385192/50653"
    ],
    [
      "1609384790408121247",
      "26381883410745417775096616"
    ],
    [
      "1528565309485370677",
      "-43968414426042796319733364"
    ],
    [
      "1471378285174580303",
      "-197955347484052125740904392"
    ],
    [
      "908576448021255457",
      "1330268094875518231309705106"
    ],
    [
      "15585474671147348527",
      "60648186658869770406744869336"
    ],
    [
      "943893790519400527",
      "1264556476444003641157942136"
    ],
    [
      "1689083145973349647",
      "-247443371956905336018409864"
    ],
    [
      "1609014410787270007",
      "23669173735396903410893936"
    ],
    [
      "1846583780015794056847/961",
      "23391127706546805029693737642376/29791"
    ],
    [
      "1532927567793358387",
      "-17566511609873756010852424"
    ],
    [
      "6751145653514428687",
      "16293447622047650076302076536"
    ],
    [
      "488029372155137047",
      "-2061235914459270979570635184"
    ],
    [
      "-886061278733770978913/1681",
      "-233722612363883599846106344460744/68921"
    ],
    [
      "1469934113376424909",
      "-201259957567302960716732218"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1370/199 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4765105671341170713012T^8 + 114715794415427693698302T^7 - 1289703173484205490556069T^6 + 1970946774680673720492576T^5 - 1710136570699445082168780T^4 - 705937567588433468644896T^3 + 1908320361802866590386896T^2 + 127404060867858778875648T - 648856125950076308077632,\nA6 = 96897205978949562584426677136484T^12 - 5182597562294583468083790262057896T^11 + 84877162983356922665937799396845291T^10 - 478870362976518748392317900380853010T^9 + 1861233683275843787028761356431736485T^8 - 1364843279709253439363789384039551872T^7 - 1311792976812619745745993240617168352T^6 + 735145326496711370457296224143481152T^5 + 1094740667609718961081479717092760480T^4 + 53782848467549070290540339428638720T^3 - 759905051149062814344760081603028736T^2 - 65476590517227188924250720852312576T + 200491211946380337902432377627289856.\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": "2026-10-15 21:29:58",
  "updated_at": "2026-10-15 21:29:58"
}