{
  "id": 5573,
  "curve_key": "10067921779047510422608976108736:-22433017081095955019497687455325796596584293760",
  "ainvs": [
    "0",
    "0",
    "0",
    "-209748370396823133804353668932",
    "25964140140157355346640841962182634949750340"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 214.16072129340003,
  "faltings_height": 15.87477391975805,
  "conductor": "70837156940213724274846615559570427920594397258667876456527444647304",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "29",
    "37",
    "53",
    "71",
    "181",
    "199",
    "1576914089",
    "11409169993421",
    "2335474199537305821303840572333"
  ],
  "discriminant": "299348954134112416570638371379844297820172430417941930954255801495895751958422619121489152",
  "regulator": "16381187384547454219.545582972861372103769282735585288835050978120497186258476139",
  "points": [
    [
      "397173855317854",
      "-2304470376337810820174"
    ],
    [
      "131426899168998",
      "817130933406144013986"
    ],
    [
      "375065216407608",
      "238149455582137023414"
    ],
    [
      "381083324576769/4",
      "20931839462814816184929/8"
    ],
    [
      "555830329660962",
      "9005661811349264187378"
    ],
    [
      "119047745477394",
      "1637454644230273712046"
    ],
    [
      "1379525760844272",
      "-48600147815916845103522"
    ],
    [
      "-6325113155090286/25",
      "990866737425615369535062/125"
    ],
    [
      "464975461614822",
      "-5381914454438342607522"
    ],
    [
      "2216636868855870",
      "102237111136030272094350"
    ],
    [
      "18349872065713320",
      "2484935763600306437925210"
    ],
    [
      "99954168490518",
      "2448987927630343811586"
    ],
    [
      "-55042803294354",
      "-6110852206603116669102"
    ],
    [
      "38585048790672",
      "-4234198234188247806978"
    ],
    [
      "2033296286169921/4",
      "-56958404575621791715137/8"
    ],
    [
      "1795222937031138",
      "73723192574064970115214"
    ],
    [
      "640211065794502",
      "-12413071963501688824478"
    ],
    [
      "68993086823478",
      "3438220888668828104514"
    ],
    [
      "55454027800170",
      "3808316896782240993570"
    ],
    [
      "-510486737291042",
      "-82083466353274030414"
    ],
    [
      "1059657295637401",
      "-31520849207700300362803"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -8/13 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": "2026-10-23 17:31:30",
  "updated_at": "2026-10-23 17:31:30"
}