{
  "id": 738,
  "curve_key": "107309910483350419800456654075601:-1096821864962330991650724383851848668375292508825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2235623135069800412509513626575",
    "1269469751113808831812336410678494175567490041"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 221.25982139271798,
  "faltings_height": 16.316095972837275,
  "conductor": "1634992090157394062979046231203825710996833965246029548763487852386502834",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "29",
    "31",
    "37",
    "61",
    "167",
    "403079",
    "3659501",
    "15929437806119",
    "2234508752346727",
    "62010492272670768451"
  ],
  "discriminant": "18923699053448771374187322251127587284235563484954725118277556743145170050467668724467604992",
  "regulator": "91446645825001322758.185080154547684559780342684784416373177717971050253840924635",
  "points": [
    [
      "-1721109311031716",
      "-4349922869857991908595"
    ],
    [
      "-31465663064561828039/18496",
      "-30726385035563916803665631129/2515456"
    ],
    [
      "-1693275654637376",
      "-14144459243242648837109"
    ],
    [
      "-25167999406043531/16",
      "-1913573855193503488201571/64"
    ],
    [
      "-1454369273941514",
      "-38008209230150733884579"
    ],
    [
      "-278613934726796663/256",
      "-201224611915679431969914371/4096"
    ],
    [
      "-979256578671998",
      "-50196281590203492836471"
    ],
    [
      "595997557299994",
      "-12196309433189880537275"
    ],
    [
      "912358458254303782/1369",
      "-440284626761681226265044791/50653"
    ],
    [
      "733670983668502",
      "-4916634404644238608931"
    ],
    [
      "6738059999057074/9",
      "-105812918225215923264233/27"
    ],
    [
      "944000954905564",
      "-523750081740825521129"
    ],
    [
      "944228543449924",
      "-611634680233563155009"
    ],
    [
      "48096793073341296/49",
      "-1563194409272788564711965/343"
    ],
    [
      "1000840570247800",
      "-5872925560704301260221"
    ],
    [
      "1098792438831838",
      "-11815469964252406992587"
    ],
    [
      "1401516201180880",
      "-29818327770617315444069"
    ],
    [
      "2190620068284502",
      "-82972599590894280308771"
    ],
    [
      "2788263238596256",
      "-129279043842795015540107"
    ],
    [
      "79011716118192613/16",
      "-21289391738541849181771529/64"
    ],
    [
      "12168411187847374",
      "-1332608328766037143423859"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-13/47 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 21 listed points are certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:41:35",
  "updated_at": "2026-09-16 17:41:35"
}