{
  "id": 4202,
  "curve_key": "68671129133807890757785932989023764476641:-18339945707420840080444083432653265001104881795381324975156689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1430648523620997724120540270604661759930",
    "21226789013218564907802172151565455052046531129511330241252"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 282.1283741722595,
  "faltings_height": 21.403676459073967,
  "conductor": "70478760662067086348938551878327869798723425742982584373150895811260297459676567219230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "43",
    "61",
    "361801483938649247",
    "52844667606505809421",
    "4673786882132408316677531614144453057"
  ],
  "discriminant": "-7245091667063850944674191560089578741141343902693415983553638991735353157509322457053223791216778190123906086400000000",
  "regulator": "491970832708754827634947.09006033095635740216685275378974552036818706683551488311737480",
  "points": [
    [
      "22354737381052709844",
      "-20406999992942230009384358922"
    ],
    [
      "21609064501199951844",
      "20054962313619591220674495078"
    ],
    [
      "26842682846179204644",
      "46532704229340348497671991478"
    ],
    [
      "-43414134428823183276",
      "38868460106781345898242785718"
    ],
    [
      "2633925202921288344",
      "132200003136590609616850137078"
    ],
    [
      "-33361318507984853406",
      "-178394817148106057016091448172"
    ],
    [
      "-11632452301562844156",
      "190511697010445639051249787078"
    ],
    [
      "22217881498367419614",
      "20206857822122601144130971288"
    ],
    [
      "8527937480749077294",
      "-98216639228137601107725312822"
    ],
    [
      "-5321898557867458356",
      "-169380711122085433794796489122"
    ],
    [
      "-17488884531624172456",
      "202232704336067538768076825778"
    ],
    [
      "26263727478469271694",
      "-42058397638171676264471184822"
    ],
    [
      "29417537855547872544",
      "67810914355390737061026320778"
    ],
    [
      "29287033993594691844",
      "66691193435919876274544865078"
    ],
    [
      "24148390997367913344",
      "-27585094319682916107337562922"
    ],
    [
      "14330249149351698444",
      "60564366181890770372952910878"
    ],
    [
      "-37799943146855256156",
      "-145929138849936484309885934922"
    ],
    [
      "23712739726434900594",
      "25213583728889085845621797578"
    ],
    [
      "-1882579387245272838204/289",
      "854774193182178036919813366302294/4913"
    ],
    [
      "17502707309472664644",
      "39350087245903449014745613878"
    ],
    [
      "1531561177139084484",
      "137982809900246468360252427318"
    ],
    [
      "22503424492045964244",
      "-20691175090828824111568920522"
    ],
    [
      "-42890549591067402156",
      "60717936835049254645136793078"
    ],
    [
      "826638510004407005844",
      "23742504170566595338193479257078"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -511/37 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -154503213541262535600T^8 + 4159635009352858651680T^7 - 21187086453270000393696T^6 - 687438318305734637863392T^5 - 4576470188855512350897360T^4 - 19322004287067422371639920T^3 - 39029689014386535692132184T^2 + 4186478995367154403195512T - 1679949255743694529867467,\nA6 = 747141710909816776767093360000T^12 - 29305404314392232038648503024000T^11 + 301598848438544320323778700280000T^10 + 2292679730804159433657382244285760T^9 - 4484131884783219751251582549192624T^8 + 544733850758018343321283421195576736T^7 + 7256453148985237089497289163544883552T^6 + 31881087967205708307154627785355135968T^5 + 53417637701365905114499013007709555776T^4 + 36362990355034819792007607408188452080T^3 + 65566855132366254216911881386291117144T^2 - 854195394262226327944905852404523432T + 424114741036883895390965869842474630.\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": "2026-10-13 01:24:38",
  "updated_at": "2026-10-13 01:24:38"
}