{
  "id": 1923,
  "curve_key": "60421905455271543466428863376:5650459408860932456449242072492166682285376",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1258789696984823822217267987",
    "-6539883575070523676445882028347415141534"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 198.8134476693916,
  "faltings_height": 14.626587453345172,
  "conductor": "425237262681943850014675499511718426424003280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "47",
    "53",
    "67",
    "71",
    "149",
    "337",
    "433",
    "509",
    "673",
    "1277",
    "2371",
    "18301",
    "178643"
  ],
  "discriminant": "109178821322378504844239369490466518426651065556313973548490158716964663972398720000",
  "regulator": "3030355423531.707469599057622555159431703673744976899434751569400",
  "points": [
    [
      "6762411620205583933562849794220341/173316674835086601025",
      "139627201832008942569458888829756866995962732723264/2281710402751994423359596582625"
    ],
    [
      "-37771279707539025771775904719/1234810393337161",
      "-2509162913551666630699579518264824436207620/43391075461706310371909"
    ],
    [
      "-21080598563627159605493/825355441",
      "2243127637469456405872351240269150/23711636464489"
    ],
    [
      "-343267288223329061230706990645203573847/11615335656166907627319184",
      "2756946667896615214949133305444728232898064093608756057195/39586549301927231135057504741061714752"
    ],
    [
      "-5669866047523937810865609923/692126701506601",
      "1033622920829027772115803277883249812862400/18208677593372812594901"
    ],
    [
      "-29736036300610",
      "67808421414293907256"
    ],
    [
      "89917014817627",
      "779268133219662327150"
    ],
    [
      "-116460803682606936803/15217801",
      "3053291997700970875746901105920/59364641701"
    ],
    [
      "231307433035257016124353/4270230409",
      "-80975492410017508893713689221654180/279046746536923"
    ],
    [
      "489361355289333371368237/28718881",
      "342328899307000461494294874513110400/153904483279"
    ],
    [
      "49047278262929017",
      "-10862311552622060196886740"
    ],
    [
      "-9034704834083070827/316969",
      "-14031547388947139104442450880/178453547"
    ],
    [
      "221976961600867",
      "-3263691144131794179090"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-7 family with u = 28/5, (p,q) = (3,7) (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12).",
  "created_at": "2026-09-25 19:15:47",
  "updated_at": "2026-09-25 19:15:47"
}