curve #1951

y² + xy + y = x³ − x² − 5402916719086617828375837827547110441856966557762x + 4833725859886565634383924531696717238724057019566476908693058963652612161

a-invariants: [1, -1, 1, -5402916719086617828375837827547110441856966557762, 4833725859886565634383924531696717238724057019566476908693058963652612161]
rank (lower bound): ≥ 19
torsion subgroup: ℤ/2ℤ
conductor (N): 793627946783274194398421134715935644462180937975502965229114197476637198622092806630
discriminant (Δ): 395457942113139520701351377166813837930102751614823430998185580314665964744281200608030373263534933305307675994894856634155682692213400576000000
Faltings height: 26.6676
naive height: 348.2467
primes of bad reduction: 2, 3, 5, 11, 13, 19, 41, 43, 47, 53, 59, 61, 97, 239, 283, 331, 347, 373, 383, 1597, 4003, 4357, 4703, 88259, 1338923, 210728940797, 1296544412161
regulator: 312157990704916144571.0879165615700121992371539259442207742420103801793330390
submitted by: dujella
submitted at: 2026-09-25 20:05:10 UTC
last updated: 2026-09-25 20:05:10 UTC

Witness: 19 independent points log in to add more points →

(1336029600818931024308321, 6982484452074243346987552859255199)
(1630926883548284909109581, 600085698640165416761663370054568059)
(786615965542165440298961, 1034618520128380805345711459365818399)
(1353258908712003226771181, 20415869217081610498319216938503159)
(1355148419151889572147281, 24561709531635368236158281650671759)
(1145987795332272568193381, 383485712083352528350867755591748359)
(1396596533826252282615281, 109851390417013090094142637486054959)
(1348132837440840404135681, 7537547675555604912269657249988159)
(1411876165006009074652481, 141075971817791097581854810619114559)
(1370098423316701523847681, 55726239232128811357373652069156159)
(1128034573609557710890241, 417648334357021838786139121897798719)
(1067704454245305073516481, 531209003211532081789617478275016959)
(1351340422064499097757441, 16035496391810410639288149386712639)
(101431820565704004177431, 2070444820150954977072985628719278159)
(1510136400035377410685481, 344192907362529271265323346605808559)
(-1269076212698534526624319, -3105885159866903190847789391243843841)
(-2315970644293850285352319, -2219122405863341885580517167833963841)
(1655529684705243828561801, 653052122387568178405611813153584519)
(1334719710439428308798081, 10885471619868597645004968593786559)

Commentary

found by Elkies - Klagsbrun (2020)

last edited by dujella at 2026-09-25 20:05:10 UTC · history