{
  "id": 5965,
  "curve_key": "22385529523737497532195949441:-3299867374755024240534489694642197737277761",
  "ainvs": [
    "1",
    "1",
    "1",
    "-466365198411197865254082280",
    "3819290943003305959563728777095724846825"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 195.83463677263663,
  "faltings_height": 14.201886623541897,
  "conductor": "134839402029595877206865360629144771588528787924637226552673130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "97",
    "627030981011010819728963213",
    "17181670530713902937681650211"
  ],
  "discriminant": "190122256256735657580913152578350504654076441371336498104551452898415765072000000",
  "regulator": "775341972267552164.055366073001379245377020471826521764667652904159912468152391",
  "points": [
    [
      "5107126390243",
      "39632216414296465603"
    ],
    [
      "407057125804393",
      "-8201312140991032326147"
    ],
    [
      "154376517318373",
      "1900247659009042496973"
    ],
    [
      "13685045107343",
      "60849254784056103"
    ],
    [
      "18797702398693",
      "41169552649665627853"
    ],
    [
      "-9941441260907",
      "86447087731766171053"
    ],
    [
      "7663782837093",
      "26368360645360583053"
    ],
    [
      "43060795595447/4",
      "54464870750834997699/8"
    ],
    [
      "-67670854122343/49",
      "-22908509677021169084421/343"
    ],
    [
      "7642556448613",
      "26485088946821219853"
    ],
    [
      "15091375103693",
      "-14773412022104097147"
    ],
    [
      "-24458533292107",
      "24378681959304788253"
    ],
    [
      "14022091865813",
      "-6073376246165219667"
    ],
    [
      "18741175640933",
      "-40762162895875807347"
    ],
    [
      "-15115261318357",
      "-86111095285736627397"
    ],
    [
      "-5114595343827",
      "-77915124845948523347"
    ],
    [
      "1948011307682687/289",
      "-153958003778587341568281/4913"
    ],
    [
      "10491062264593",
      "9016422431246205553"
    ],
    [
      "3662354773493",
      "46480302816266231853"
    ],
    [
      "3594114042138713/256",
      "25595654957822869125813/4096"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -10/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -118937177346945845659707T^8 - 178627984651034750261448T^7 + 538725115408622183167176T^6 + 932687723092640101942896T^5 - 785596976914037914856880T^4 + 532319133790622065220064T^3 - 1885695726240745162373664T^2 - 977032720488720551059872T - 121021369855000800926832,\nA6 = 15700020995297278065702962968986006T^12 + 37259362275892277501775777129653976T^11 - 91123084323059325303034614872980296T^10 - 338078840866824691573377389572497840T^9 + 146594450200795609255542798171153120T^8 + 1165683634482625362035291597494076064T^7 + 136953122145599945469132137315051424T^6 - 2655038031228910497864633944351855904T^5 + 509959130847733176223681554198385680T^4 + 1350975024523639142563101930559667520T^3 + 692961598461491245602665065671309504T^2 + 172025669836703204112379176286164864T + 16373121443610735589881083198960256.\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": "2026-10-27 01:49:42",
  "updated_at": "2026-10-27 01:49:42"
}