{
  "id": 5974,
  "curve_key": "21143591720954800531596841:-95278782557948964844976119398814955605",
  "ainvs": [
    "1",
    "0",
    "1",
    "-440491494186558344408268",
    "110276368701293112797910517590298102"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 174.9401372985631,
  "faltings_height": 12.474454048239197,
  "conductor": "1718624170408192878224755167584234896649934401234760775253838",
  "bad_primes": [
    "2",
    "3",
    "13",
    "31",
    "47",
    "188653",
    "2585838225641182746054380505424976893242818411371"
  ],
  "discriminant": "216566766459830512000974955554360178512547041880674835384522600687322532",
  "regulator": "232690734007016167.0501200382599826956169036289111835919870053877422723472341",
  "points": [
    [
      "264008476061",
      "111285073224613233"
    ],
    [
      "511355024783",
      "-136894255991712495"
    ],
    [
      "-359125099822",
      "-471329063848430154"
    ],
    [
      "450396426212",
      "56978850668063841"
    ],
    [
      "-483036093769",
      "458634965090217705"
    ],
    [
      "-34783581385",
      "-354339023456648097"
    ],
    [
      "-297848672155",
      "463738090465630341"
    ],
    [
      "240819937870",
      "-134771795137470637"
    ],
    [
      "234549040796",
      "140935388808881898"
    ],
    [
      "968207732549",
      "-769033907554857363"
    ],
    [
      "-696918475477",
      "280665555484826295"
    ],
    [
      "501136707830",
      "124033543116545358"
    ],
    [
      "27745140140909/49",
      "-70626553832699369121/343"
    ],
    [
      "427375479068",
      "-9008608165541910"
    ],
    [
      "480134505635",
      "-97294634834645979"
    ],
    [
      "332221180829",
      "24562394845353297"
    ],
    [
      "-72070816501",
      "-376362289293856713"
    ],
    [
      "337712746181",
      "5734035584867613"
    ],
    [
      "72563859503",
      "-280525778062689825"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 7/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4505943394275807984192T^8 + 52980291620776162887552T^7 - 331691816140954740938736T^6 - 523944665267054297606640T^5 + 845300299497227347100760T^4 - 1642234256419962398088672T^3 + 246946848567560622997776T^2 + 5627761674121177889229000T - 4516338503114727494506875,\nA6 = 116816047040551151889517539873024T^12 - 2060050809167332071751695581116416T^11 + 18412638495454417247201410610781312T^10 - 40800313765336647939058137401925120T^9 - 11012846950180332303068155006051056T^8 + 1064724795536936542804757035648974528T^7 + 74801504042697709025857109411374608T^6 - 4178046358163385705380531645236403664T^5 + 393751226136259880507039408579785464T^4 + 7329668110287569443800658599168206880T^3 - 1977247101474084220684442672481828000T^2 - 6488561441371188321193822317113175000T + 3856841937412106545376986975288593750.\nIt is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration 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": "2026-10-27 13:49:18",
  "updated_at": "2026-10-27 13:49:18"
}