{
  "id": 4230,
  "curve_key": "1133367400817074488774548391608736576:-1848163909492663558312159345073935764872859274970509824",
  "ainvs": [
    "0",
    "0",
    "0",
    "-23611820850355718516136424825182012",
    "2139078598949842081379814056798536764899142679364016"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 249.9075753731553,
  "faltings_height": 18.856806048100424,
  "conductor": "146954943734085658569266296693767955932028661605823373833844075363529407736700157718105920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "47",
    "59",
    "613",
    "3555869869037",
    "4092513265733",
    "1423564104240445042058874623429533002566377872601729"
  ],
  "discriminant": "-1134186837575672884356463499602074052823250021137983885342779082105214743258517728044807046078985472000000",
  "regulator": "10472542313942194830406339.724476477756222552708539660971498597598694532586531095426645",
  "points": [
    [
      "55654725527237112",
      "-31580956840366245941288940"
    ],
    [
      "2156886165493000602",
      "3159966162746193304291128600"
    ],
    [
      "57018687327565136472/361",
      "332501009406393850994417155500/6859"
    ],
    [
      "330668107715114433/4",
      "-219394451618660768807417025/8"
    ],
    [
      "107441040213303597",
      "-29025057092797715706966405"
    ],
    [
      "277555554845640312",
      "130259578217726502445990740"
    ],
    [
      "13156277060953477",
      "-42786821927946676793558975"
    ],
    [
      "189117913367507652",
      "66615111979824706880013600"
    ],
    [
      "105942109278706746",
      "28751663938797880169825400"
    ],
    [
      "-86606930826612648",
      "-59450888059781730705104100"
    ],
    [
      "346182444126924282",
      "188288012753807956263604680"
    ],
    [
      "-734251494639419367/4",
      "-135793005386916128715652125/8"
    ],
    [
      "56784457447927002",
      "-31327211873307098338233000"
    ],
    [
      "-98831223635709198",
      "59222620863337388310751800"
    ],
    [
      "296931712773607992",
      "145972554621873046762408140"
    ],
    [
      "-1373434231892387809958/7921",
      "22517310939584942886530849448200/704969"
    ],
    [
      "-46834958971168008",
      "-56055366830215811466547860"
    ],
    [
      "7345784352712582789368/24649",
      "568362194414659154006630121410940/3869893"
    ],
    [
      "-180582316915812648",
      "-22675347909497643234779100"
    ],
    [
      "10516987621168796073/4",
      "-34050204819350837691353944395/8"
    ],
    [
      "-1598509038201786572/9",
      "-729430360192367437357404280/27"
    ],
    [
      "235022699371382002",
      "97833536209474203500243000"
    ],
    [
      "151981981298954712",
      "45398970471534538557941340"
    ],
    [
      "-10409431572388398",
      "-48823522048888318597895400"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 103/40 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10669947921935414766592T^8 + 11909462495223346810112T^7 + 29290850738695015599056T^6 + 749826724411797003953776T^5 - 2800296645908250177432680T^4 + 5291011042236720751525024T^3 - 9053743075112346775820704T^2 - 1373686135035664689321352T - 153062929487822447776267,\nA6 = 424084459520579325699737587892224T^12 - 702971076900016054991835746922496T^11 - 1428460164091780099364248773693184T^10 - 45531551300070380060674898437602560T^9 + 178145138683306119166957105019549520T^8 - 224307849011465835658368095576866752T^7 + 1890363249575504635685922631864051728T^6 - 8402714629932209203714457518206796848T^5 + 10932033646871752694840038266436614840T^4 - 1045636958253350245306227479236779680T^3 + 3911537622199302231442442603656239344T^2 + 397823992391227625022128206594583384T + 16543056563137220502197778370669126.\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": "2026-10-14 19:28:16",
  "updated_at": "2026-10-14 19:28:16"
}