{
  "id": 6163,
  "curve_key": "537564652056279792079426941616:-388139590868916157725804181018894992474264664",
  "ainvs": [
    "0",
    "1",
    "1",
    "-11199263584505829001654727950",
    "449235637579760338354041485347387171195156"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 205.37053963950913,
  "faltings_height": 14.997926663302323,
  "conductor": "76562065165874876762554361876614544985049246366340063438470485",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17",
    "29",
    "31",
    "73",
    "18401",
    "35518240357257255057122022562925008092604825194023"
  ],
  "discriminant": "2714588694938877865025458574854214583015935684257815031146657680958048835304089453125",
  "regulator": "525414918464880842.649061707359132291649221043955328016216044367002320676534768",
  "points": [
    [
      "70176440004725",
      "94400209918311180187"
    ],
    [
      "69133995436385",
      "-73568851426706090648"
    ],
    [
      "280844619902405/4",
      "-760452797341540695739/8"
    ],
    [
      "79197625865225",
      "242958768742749754687"
    ],
    [
      "54824442882970",
      "-5399070442977931493"
    ],
    [
      "77253599239850",
      "-212393170875236663813"
    ],
    [
      "53194225217285",
      "-63397393139578965548"
    ],
    [
      "168489634373975",
      "-1829067270481062930938"
    ],
    [
      "71878841463980",
      "-124949819101324854893"
    ],
    [
      "19291758030725",
      "-490267279312365545813"
    ],
    [
      "93513508762700",
      "468730115702431127212"
    ],
    [
      "415536359265725",
      "8218661153880675969187"
    ],
    [
      "69069401066225",
      "-72183531331463956313"
    ],
    [
      "77351999587175",
      "-213945991882083375863"
    ],
    [
      "112126380334820",
      "776654403708868543267"
    ],
    [
      "75776576224760",
      "-188970023873670547148"
    ],
    [
      "100337024630225",
      "-579378722710055959688"
    ],
    [
      "-229778521951315/4",
      "7602157540481993426591/8"
    ],
    [
      "-53453667092800",
      "946120750511965329787"
    ],
    [
      "-119583190073650",
      "280041107225835050812"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -7/13 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -105011986328338530184252T^8 + 1624598433710275617978304T^7 - 6321400765862790768797668T^6 - 6714644299565372036732264T^5 - 5697585703504986516411400T^4 - 19474800058502498278832768T^3 + 22490650492223580303426560T^2 + 23684368560400255356574528T - 19516759643691525209970352,\nA6 = 13613297573190764450387734076665396T^12 - 279747285467910413302835983826594288T^11 + 2042517619565912841517522343157110840T^10 - 6782403520591044024313048723487823440T^9 + 4706947676894032497276227735499747396T^8 + 67181083628538099142151895496763512032T^7 + 7944774490731402629902892096898574128T^6 - 127085975499992571495595833570771036000T^5 + 2577039428202679942233522288128755296T^4 + 133317246010924356002971327979124643840T^3 - 38493179266151915812989454964700702464T^2 - 65224947674167075345316672819115241216T + 33481436299182969940397985534717172096.\nIt is a 2-neighbour of the fibration given in curve#728: 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": "2026-10-30 00:21:44",
  "updated_at": "2026-10-30 00:21:44"
}