{
  "id": 4585,
  "curve_key": "9731514013768803227984119252088622016:-43764409047375314485621535679817742848797365736655431040",
  "ainvs": [
    "0",
    "1",
    "0",
    "-202739875286850067249669151085179625",
    "50653251212239947253741263422690883658440567389032059"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 256.2368318598254,
  "faltings_height": 19.37885425295582,
  "conductor": "152644332038686018241286373503957697870476328219471932265402133554019543264948099391096",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "23",
    "31",
    "43",
    "234948323",
    "214203636247232353584559",
    "204964478153866583233943714913921515910005053"
  ],
  "discriminant": "-575072978663020819214862706492392574346170950939057945877622025819877039800639910384445944826854900491725568",
  "regulator": "1821668140328206901342234.0819031584448730261418047308717423051803085785352475222578409",
  "points": [
    [
      "-273290436664687386",
      "292657985174162036709396207"
    ],
    [
      "2189566035786345363",
      "3178672228478801143503569610"
    ],
    [
      "-423273274376779225",
      "246239456933375630473608678"
    ],
    [
      "762406063798857807",
      "582444487865993108853052374"
    ],
    [
      "-43750707950698117509/121",
      "-368587691269634387587441073214/1331"
    ],
    [
      "562941385044999597",
      "-338999115701078644286616246"
    ],
    [
      "1753448321914662429",
      "2255277872691336947852048742"
    ],
    [
      "-291694145105389803",
      "-291500173463521843909064046"
    ],
    [
      "-316974252548749194",
      "288217487359062855097767081"
    ],
    [
      "194412819601054971",
      "136330900028127217093864806"
    ],
    [
      "1842915337669203021/4",
      "-1876925866404121918090629651/8"
    ],
    [
      "12701498228879923701",
      "45239181984409324722780448206"
    ],
    [
      "8577173537207041095",
      "25086179735519878248617584422"
    ],
    [
      "-2669985197145072639/16",
      "-18083635193590105048901032041/64"
    ],
    [
      "5053689075415110291",
      "-11317956623278079763958813494"
    ],
    [
      "376633915138015227",
      "-166496933688738734287037286"
    ],
    [
      "154131482943073200789/4",
      "1913407954906620737174342132673/8"
    ],
    [
      "-109634496488997333",
      "267512166262030866144007494"
    ],
    [
      "494136587933171694",
      "266694337715873279527742427"
    ],
    [
      "295443851612884485",
      "-128621264097413546293056222"
    ],
    [
      "143715815734817277/4",
      "1666908993608547806196772875/8"
    ],
    [
      "1706748473974132827",
      "-2162491414744059369238909914"
    ],
    [
      "438118717670235",
      "224865353405442754691146278"
    ],
    [
      "1289620670389782342759/2809",
      "-34705432981195522881441294577662/148877"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -139/93 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -94521237307405223348592T^8 + 194603007768925915807776T^7 + 374678018163025368194124T^6 - 569211691896707346596088T^5 + 55463370301014723924120T^4 - 1135612908646444410668928T^3 - 2702507543729482509654336T^2 + 609092474805433024526016T - 184694377125002807554992,\nA6 = 11265741534554236438342976060251776T^12 - 34833166213267258548363680994916992T^11 - 69502033189823387959197312852122064T^10 + 265587490260133017697161120524802480T^9 + 273144084685427886803017231992231060T^8 - 1114854493674664679669934784078225824T^7 - 766273999597311933358466543970856272T^6 + 2407762999977059159006184076291662816T^5 + 1357060199643920217443950358505612000T^4 - 540509467373796107556447739286515200T^3 + 808090270114106954000628418781159424T^2 - 154315127645781466989761857773289728T + 30433563297067405810172392059479424.\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": "2026-10-18 10:32:32",
  "updated_at": "2026-10-18 10:32:32"
}