{
  "id": 5945,
  "curve_key": "625095398323527100841638177621681:-15357452736351028598372869207412831519113268769385",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13022820798406814600867462033785",
    "17774829555961837570289087641345116037796299001"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 226.54637119568258,
  "faltings_height": 16.76850059350701,
  "conductor": "26503755687286559852342918698731162913797844441989908448156937436238246",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "29",
    "5281",
    "280498553",
    "6042663075588046909010201267317102620868760122282709"
  ],
  "discriminant": "4861737515087429031868622357083439576919051890912951902367202823574653762532616417290781622272",
  "regulator": "180730798751150219364.1301331985079038083382882779684786492886379106407395465227972",
  "points": [
    [
      "-3629282358422950",
      "-131280383629376792325901"
    ],
    [
      "2697642295366790",
      "-47701147852959573107521"
    ],
    [
      "-3820047564126022",
      "108524534504185210719923"
    ],
    [
      "1587131072681618",
      "33224469772877132030819"
    ],
    [
      "1844083603739522",
      "5543618136340950355139"
    ],
    [
      "-2198729431638826",
      "189153184864170479038415"
    ],
    [
      "-1233534291264322",
      "178779113925049039137623"
    ],
    [
      "2318081075399588",
      "6563799347644918657529"
    ],
    [
      "709515055872394",
      "-94298039832573011494445"
    ],
    [
      "216768011937248",
      "-122319598527614519386741"
    ],
    [
      "3683566250306714",
      "-140660819403940679767309"
    ],
    [
      "40283554769200514",
      "8053812952757077173248195"
    ],
    [
      "1427653697945246",
      "-45744814959029311228489"
    ],
    [
      "41475730651020170/49",
      "-29422515800291997665064763/343"
    ],
    [
      "3074982023912570",
      "82495008328451695501139"
    ],
    [
      "22487526319024538",
      "-3331158203478102919156621"
    ],
    [
      "2461359352160480",
      "25151861492681157280661"
    ],
    [
      "-3783224120288842",
      "113554424268824168654639"
    ],
    [
      "1241666107966874",
      "59322457978884293389811"
    ],
    [
      "2323170654163130",
      "-7683075459569013907789"
    ],
    [
      "4408971662143820",
      "-214624602452414277598861"
    ],
    [
      "1682125250512478",
      "25069174512692252250923"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -336/139 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -24031029665327797232767T^8 + 179305869982048445443572T^7 - 15434043446921367581904T^6 - 1359491595553384291321920T^5 - 1251177099291190680208560T^4 - 793870677479698730348832T^3 - 465983991977317682237856T^2 + 1581044404633777347981120T - 513268853367954448263600,\nA6 = 1464980610683190207683635064387170T^12 - 15226098350974251104399011548495212T^11 + 31182187814980858871948850733079604T^10 + 94882057085868263070543071690124440T^9 - 382383456053978226203046668114059644T^8 + 119987179832555651967492958730573328T^7 + 2833926355389365701285515892492966272T^6 + 1391513510216999650767496184555750016T^5 - 3206877893714253625843008218509021824T^4 - 325665422393502655104433213009299840T^3 + 1960986866227523419821124223062684800T^2 - 999490438443489710935366277087328000T + 167924010299517718017234405479280000.\nIt is a 2-neighbour of the fibration given in curve#4647: 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": "2026-10-26 04:50:36",
  "updated_at": "2026-10-26 04:50:36"
}