curve #4107

y² + xy + y = x³ − x² − 1091761463896191699101735035623460056239305376481737x + 123420762167481262190297515633940819970225991624542571542273452424110905131849

a-invariants: [1, -1, 1, -1091761463896191699101735035623460056239305376481737, 123420762167481262190297515633940819970225991624542571542273452424110905131849]
c-invariants: [52404550267017201556883281709926082699486658071123361, -106635538512703810532417053271904392252697849757630014117856890746741860713862641]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 374785364077444172381903170722631268547812541904984566738340877113861929593075923530
discriminant (Δ): -6497235396305516755068542582370764748280622394048180226878645206129576257411904321392464187857722129160310648247909798842421747326981930620791458500000000000
Faltings height: 28.7696
naive height: 368.5421
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 31, 59, 73, 79, 193, 223, 389, 541, 643, 1097, 1151, 1447, 1831, 1913, 2273, 2591, 5227, 5399, 7853, 10601, 20020291, 161738747
regulator: 72997233807793887320914.7637322334576954005324514829839687887294246512021818462
submitted by: wgxli
submitted at: 2026-10-09 15:21:58 UTC
last updated: 2026-10-09 15:21:58 UTC

Witness: 20 independent points log in to add more points →

(-57042684897657638776943593, 9402446415339112287658032922983353196)
(-57044931413368352099748613, 8302300773410723291372214523058857896)
(-57009118545467084632715473, 19473782488288466250882147645893975196)
(16713807191353887457161767, 331424646303465568943113524406878435036)
(17451613599786222926766527, 331183945494398959608960305171848895196)
(18605740824080652955397207, 330981188973321735833390986869403926396)
(30387782403626530690684707, 343955167043474487069566266225248988896)
(56470603386465638430725957, 491781537858372962940678196847081188896)
(59187944184773485001959407, 515896894266245667095155251208940590196)
(60991302809072213443758107, 532650669038369120143421713876883807496)
(-14423303035305234270808393, 369008217767184717764748175539670104396)
(-19041206072992058242396543, 370547559908934759128448113355901907646)
(-27135160235938313590093771, 364781861930049667557684916545625850592)
(-50139032896836882903877483, 228287049973316173581439921784292925536)
(104804857353320273118384707, 1077117218604984903906806216160290488896)
(145251694746242961502688277, 1740508195527549278646438823743583174026)
(830047365805162921210743207, 23897742645089997073274946582495186210396)
(66165285149461372692660527207, 17019438531664091393401017220705918661526396)
(5170111861638901058682132983/169, 756777668056314488365072171928590663677012/2197)
(2587069666587962467009227182423/11449, 4138848461971779692382500264100818275336954428/1225043)

Commentary

2-isogenous to curve #4106

last edited by wgxli at 2026-10-09 15:21:58 UTC · history