{
  "id": 5858,
  "curve_key": "678735109308723225684090913216:-553361866753964194808446017187534709773521280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-14140314777265067201751894025",
    "640465123557824215738183061166875700495419"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 206.07008533033013,
  "faltings_height": 15.039401990724851,
  "conductor": "278126096222702109285385379201270887834334591370141638573676072",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "47",
    "53",
    "1466114537869",
    "670531338113983694486998979982123487609"
  ],
  "discriminant": "3744936300190458540026722018559099782671141731651609412434227801473648219990506956032",
  "regulator": "373508317866759637.586261229094762752120082257084506017675695727873651716911959",
  "points": [
    [
      "346915562410229/4",
      "-2062346511642070704687/8"
    ],
    [
      "4076256296949959",
      "260141359413630047401698"
    ],
    [
      "75183801912887",
      "48236532365566739454"
    ],
    [
      "76461867079187",
      "79361345176672186446"
    ],
    [
      "80288910807695",
      "150737506631191199538"
    ],
    [
      "58956363974267",
      "108292311661771647486"
    ],
    [
      "61533396229895",
      "-57888263370936642462"
    ],
    [
      "-62302235610025",
      "1131197572188114387138"
    ],
    [
      "47380417940627",
      "277228406834358290766"
    ],
    [
      "49962183317909",
      "-242282301930257213898"
    ],
    [
      "48764418332765",
      "258613899260739147762"
    ],
    [
      "74585702045990",
      "-26871719108709952113"
    ],
    [
      "1205548220021699/25",
      "33242702745620410269318/125"
    ],
    [
      "62828539224677",
      "-7795499045036004666"
    ],
    [
      "-35948765205001",
      "1049921376545656145538"
    ],
    [
      "100391332326875",
      "-482375430115467932862"
    ],
    [
      "57873170194559",
      "126313539816524345298"
    ],
    [
      "-117448558089091",
      "-825299980035642964398"
    ],
    [
      "172820133262589/4",
      "-2655495179986180955787/8"
    ],
    [
      "61376168870342",
      "-61586502496512848289"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 15/29 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -24011570250321173399907T^8 - 356625422779304362612668T^7 - 1671152276752436694790849T^6 - 1732924520270453003282874T^5 - 1590147679200142298997105T^4 + 386386685489195171580024T^3 + 1390900315063766269994001T^2 - 109185086941693427240802T - 395834418180372108310812,\nA6 = 1216216238839692796812141066344094T^12 + 26209873296759406934598983518866084T^11 + 230543686141973991553199370733886191T^10 + 1052224609079923489090821191968978740T^9 + 2393956796589717261918365468578783320T^8 + 629549415237804682066795998544524480T^7 - 1844893995718784103700959635524244430T^6 - 226188479515226331041573622292694160T^5 + 1278208881685740455186312823654525570T^4 + 13862357385931867527612871612710300T^3 - 504285816967908504474275294387026905T^2 + 26689064927161462765535195704544220T + 94664857047267576565599696553129920.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-25 14:15:00",
  "updated_at": "2026-10-25 14:15:00"
}